 I think is start out with questions and answers from the big log review package We'll do that for a few minutes You can write this down if you want to or if you want to I can print this up for you after the fact Whichever way you think you're going to learn best So if you learn best by writing stuff great if you find you're missing stuff when you're writing stuff Don't bother writing it. I'll print it up for you after I'll leave this one open Okay Cam for the sake of posterity. Can we just let whatever it is die that we're letting die Log tutorial Number two wealth is fleeting Caitlyn wealth is fleeting For you barely we are all like dust in the wind. I think it's a Kansas song or something like that So questions from the big review, which ones would you like me to go over and give me a second? I'll load it up Provincial exam review the 2009 one, which is this one? Which ones would you like me to do now is your chance to ask Caitlyn? 26 love to 26 Okay, the first thing I would be doing is I would say I'm pretty sure there's an exponential growth kind of a word problem because I see Intensity and percentages and reduced for each meter and all that stuff Okay, so I think the very first thing I would do because I feel better now. It's no longer blank Now let's see if I can figure stuff out now. I'm noticing That in this case, I don't think we're talking about time it looks like what's changing actually is depth So I might in my real equation if I was doing this like in a physics class or something Caitlyn I might put a D there instead of a T, but I'm I'll deal with that when I need to What's the period every what? You know what the periods one yay Did they tell me what my final amount is? I think I want to end up I Think my final amount and I can either write that as 10% or I can write it as point one Now if I'm ending up with 10% what percent is my initial amount, what am I starting out with I could either write 100% Or one that's gonna be my initial Okay Right. We said when we're talking about a percentage if they give you a final percent. Okay, if they give you a final percent remaining Then probably your initial amount was a hundred percent Caitlyn I'm reducing by two percent What's my growth constant my growth rate going to be if I'm losing two percent? 98% is what I'm keeping So I think my equation is going to look like this 10% now I think in the answer key I use 10 and 100 for some reason usually what I've done with you guys is I've used point one and One because that's not going to be part of the equation at all But I think when I divided by a hundred I got point one and one anyways of my next line point nine two Nine eight. Thank you. I'm thinking of another question already And I'll you know what I'll put D for depth instead of T for time. Is that okay, and I'm That one's not going to make a difference there at all. Is it how would I solve for D? Log both sides, but are you okay with the rest or do you want me to keep going? You're okay with the rest. Okay, log both sides and this one hasn't got a bunch of junk I think you'll end up with log point one divided by log of point nine eight. Okay by the way Here's also probably what I would have done at the very beginning Caitlyn. Can you look up for a second kiddo? What am I losing for each meter? What am I losing each meter Caitlyn what percent? Well, there's no way That after five meters, I've lost 90 percent five is a bad answer to me Right if I'm only losing two percent each meter. No way. I lost 90 percent in five meters In fact at best I've lost a little more than 10 percent or something like that. So that's a bad answer I'm guessing probably C or D to be quite honest, but Again what I've really tried to emphasize that you guys is you can often get rid of nonsense answers and Save yourself the mistakes right next one 20 love to 20s kind of yucky 20 is a simplifying log rules question Sorry on the recording. I just hit pause and I can't remember. I was in mid-sentence. Um, this is a pretty challenging one It's it's got a number of I would consider it's about a B level question. Okay. I think I'm looking Breaking it up because I see more than one term positives on negatives on the Except I'll reverse that on top means positive on the bottom means negative. I'm gonna have this log of a hundred plus log of x cubed, you know, what can I do that right away? minus log y I'm kind of thinking a Yuck and B D yuck. Let's see what else I can do here. Um, What is the log of a hundred? Oh, you're saying this is two plus three log x Minus log y and I think I do have that. Oh see So they do like to do that once in a while mix up pure variables and some numerical answers as well with with a good base So you may see for example that base six and a 36 there or something like that Okay, there's a little extra work, but wasn't too bad next 17 sure Written section number 17. Ah the first person to ask me a written question Nope, there's a written section on this big review the last second last page Population of a nest of ants can oh, you know what? This is an exponential growth You can my friend. I'd write this Does not feel better On the written section that be at the very very end. Okay. Um Let's see. Did they give me my initial population Chica? What? 12,000 did they give me my final population? What? 300,000 you said Right sure Was your ankle you're hurt right not okay. Just make sure Okay, now the rest of this is gonna be a little bit first of all When they're asking for How many weeks? I think they're asking for total time In fact, I think that This eight weeks here. Isn't that the length of one growth period? It triples every what eight weeks. I think that's the growth period by the way Multiply three-fold or triple. I think that's telling me That okay, let's put everything together. We're gonna have 300,000 Equals 12,000 three to the T over eight Now what Chica? Well by 12,000 absolutely. What do you get called? Even oh, that's nice So you get 25 equals Three to the T over eight 27 would have been really nice because then I wouldn't have actually needed logs I could have written this as three to something equals three to something and actually solved it by equating the exponents 25 though, okay Now what Chica? both sides and I'll get log 25 equals T over eight log three and now it's cross multiple Are you okay with the step? I think I'll get this T is going to end up being it's going to be that times that divided by that when I do the math It's going to be eight times the log of 25 divided by the log of Three and I turned my graph and calculator off Sorry, what'd you get? 23.44 and we're in weeks. I think is that what the answer says by the way answers on the last page there Yep, okay. Oh and it said accurate to at least two decimal places Oh, well, you're on the internet now. Oh okay Did You have a calculator from the array? Okay. Yeah, right now 15 I have no idea what question you're talking about. Let me look at it first and you can start explaining stuff 15 written or multiple choice This guy here. Okay. I don't know. Let's try it. Oh They have a simple method for taking a question that everyone well Most kids will get right and making it harder. They replace everything with letters So Colin, let me just write one with numbers next to it and we'll do the same stuff with the letters If I gave you this Get just hang on if I gave you something like that What would you do and let me pause first? It seems to me Colin here. You know what I would do first divide by 40. Wouldn't I? Yeah, you know, I'm gonna do first here divide by Hey, first thing I would do is I would write this as That and I just saw some lights already go on because I think you started to glance at the answers and figure out what it's good Let's walk through it. Now. I'll take the log of both sides Right move the X to the front. How do you get the X by itself? Okay? Now if we had numbers here if If we had numbers here This is what we would write because we would go to our calculator. We would have changed that to a decimal already Right, we would just go straight plug-and-chug. Ah, this is the algebraic version non-calc. What's dividing inside a log the same as? Yeah, you're ready. I heard you say log of C minus log of a divided by Log B common mistakes to avoid. I still see some kids that want to go. Can I cancel out the logs? No, no, no, they're mathematical operations, not variables I can't just cross those out and I've never given you a rule for dividing two logs It's always been dividing one thing two things inside the same log becomes subtraction Anyways, the answer would be C Is that okay? Madison, you had a question? Simplify, I guess use my log rules and the only thing that I just thought well, let's keep going anyways I don't know. Let's find out. Let's break it up Okay positives on Negatives on the except in reverse on the top means positive on the bottom means negative. I'm gonna write No, it's actually terribly Apologize I want to walk through this question anyhow. Sorry for all the interruptions those of you on the internet at home That's my eighth interruption live with it I'm popular So it would look like this Madison log base a of one take away log base a of a and you know what instead of writing to the B I'd move the B to the front by the way, what is log base a of a? so this whole thing here would just and What's the log base a of one? In fact, what's the log base anything of one? Yeah, this is zero take away B, which I think is just negative B That's actually a nice little question And I don't mean that I like this question like this question I'm just saying the nerd within me goes. Oh, I like it when something that ugly ends up being something that nice 14 someone said okay 14 This is the log definition and I have to go a little negative on you and say If you don't know this you're in trouble Okay, you need to be able to do this almost in your sleep You need to be able to go from exponent to log to exponent to log to exponent to log to exponent to log and I Apologize, but I got to be really honest and put a little fear into you and say This is as close as it gets to free marks. So if I want to write this as a log rhythm Well, first of all my base is my base is my base is my base is my base is my base is my base It's gonna be log base q remember 14 log base q of P equals R That's the logarithmic form because it's that to that equals that Okay, you need to be able to flip-flop back and forth almost in your sleep without thinking my friend Sorry, I didn't want to come across as real negative, but this is crucial crucial crucial Next 12 No one's gonna dare ask a question again. No, you need to Don't undo. Let's try this again. I thought I clicked there That's better This would be fair game on the calculator or on the non calculator on the written section So on the written section, I think I'm gonna give you some kind of a log equation What do I mean by log equation an equation that has logs in it, right? Is there logs in everything in this equation? No, so I'm not gonna write this as one log equals one log logs cancel I am gonna write this as one log equals a number and then actually do number 14 I'm gonna write it as a logarithm or x exponent. So you ready? My bases are all the same by the way, I Don't remember if I actually put one on your test or not But I've for a while there I was saying my base all the same so I can use my log rules The only like nasty twist on this that I've ever seen would have been maybe a log base nine Right here because what's my original base three if I wrote this as a base three I have on the bottom a log base three of nine I'd have a two in the denominator and I could deal with it They're not gonna give you a base three and a base seven And I'll be honest rarely do I see them giving you different bases at all in these kinds of questions So my bases are the same. What's adding to logs the same as? Yep, I would write this as the log base three of I put the X instead of X minus six X We're used to seeing the shorter term in front. So X bracket X minus six. Okay, okay If there was a log over here now I could cancel up the log I don't have a log over here, but I said to you actually one equation is the same as two equations This is two equations. What's the exponential form of this give you hit your bases your bases your bases your base? three to the power of Three equals what's inside the log really carefully? What is three to the third? Not nine. It's not nine. It's not nine. So let's try this again Really carefully what's three to the by the way? I'll bet you one of those answers is what you would get if you put a nine there 27 just hang on Hang on um you get this what kind of an equation is this Priya Well, I'm gonna have to get rid of the brackets first. Let's look at it this way We get 27 equals X squared minus six X say what kind of an equation is this? It's a quadratic. How do I know? That's squared. How do I solve the quadratic first thing make it equal to so I'm gonna go like this zero equals X squared minus six X minus 27 Does this factor are their numbers that multiply to negative 27 that the negative six oh? Okay, so my roots are my solutions are nine and negative three, but I can't stop there I've got to go back and check for extraneous in the original type written e-question, and I'm pretty sure I can't put a Sorry, I can't put a negative three right there because if I put a negative three right there Did I do this right? Yeah, that's extraneous. Sorry Doing bad math at nine works though because nine take away six will give me a positive For some reason I was going six take away nine in here and going what the heck? Yeah, be I don't think you would if you put a nine there you'd have that right there which Doesn't exactly factor let's just decide we're not gonna do that Let's decide we'll remember our math eight But and those are the those are what I call the mistrakes I always do you say my students I never make mistrakes and what I meant by a mistake was the sloppy ones I'm still the king of going two times three is five What did I really add to them? I'm still the king of two and three to me or five not six I do that all the time and you see me as I'm doing the work That's the tricky part to getting a hundred percent in this stuff is getting rid of those next question, please Yo That to that equals what's inside the log we wrote it as an exponent 21 very similar question to what was just asked. I think we're gonna get a quadratic I see some logs and some not Okay My base is pattern the same So I'm gonna write this as one thing equals one thing I'll combine the logs on the left-hand side Okay, a little note by the way. I can't remember. I might be giving you a hint I might not I know I can't remember if I left it this way or not What if the two was over here and the log was over here get all your logs to one side get all your non logs to the other side don't try and Combine stuff Yep You're gonna have x plus four Plus means times six minus x That equals two Jordan my friend. This is our official log definition. We said this if you know a to the b equals c You also know log base a of c equals b and it goes in reverse You need to know this in your sleep So what I'm doing here is I'm saying I'm taking this an ugly or this I agree and I'm turning into that my base is my base is my base To that Equals what's inside the log? Okay, that's key By the way, oh Colin Carefully, what is three squared? Don't say six nine And I'll be honest although I almost always foil in my head. What's weird about this? The negative that I'm gonna foil this one out very very carefully. I'm not gonna take the risk that I make it dumb the straight, okay? I'll have a 6x I'll have a negative x squared I'll have a positive 24. I'll have a negative 4x This is going to be a quadratic, but let's gather like terms first. I'm gonna be extra careful here 9 equals I'll have a negative x squared I'll have a positive 2x And I'll have a positive 24 Right, how do I solve the quadratic? Now I'm betting this one factors You know how I know this one factors no decimal answers So although it would be easier to minus the nine over have I ever factored one where the x squared was negative? And there's a reason why we don't bother teaching you you don't need to I'm gonna actually move these three guys over to this side It's gonna be I guess more mental work, but it's still Michael gonna be one line So I would write this as positive x squared minus 2x and then I'll minus 24 from the nine and I'll get negative 15 equals zero and now I smile because I think this does factor Numbers that multiply to negative 15 and add to negative 2 negative 5 and positive 3 you said and now I got my roots 5 and negative 3 now by the way you may have noticed in most of our questions The positive root was okay, and the negative one was extraneous I'm a little leery about this one Pat because that x was negative initially I'll bet you the negative one is gonna be the good one. Let's go check Can I stick a five in here? Let's see five plus four nine that works six take away five nine that works So the five is okay What about the negative three negative three plus four? That's positive that works six minus minus three You know what as it turns out this is one of those rare equate equations Where no extraneous route path they both work you asked me this one didn't you yeah? Thank you for your full attention the whole way Okay Yep, I'm willing to do whatever you guys want right now. I'm doing q&a. I've cleared my calendar honestly till six I don't want to go that long But there have been times in the past years where I've had to with some kids and Doing dinner with some friends at seven so six is my cutoff With my former teacher that I retired with was there a topic you want me to go over I can We're good Okay, any others No problem. Sorry. What calling? Oh, no, never mind This is weird I really I've done a better job of teaching maybe starting with logs at the beginning when you guys are fresh has made a difference because last year I had about 45 kids crammed in here Like it was it was packed and and kids were Although I did go a bit faster last year Jimmy any questions? No 54 I'd love to do 54 I'm gonna try Pat you just saw it because I like this question. I like this question. I like this question Pat how would you solve this? Get read it as an exponent. Yeah, right the second version of this five squared equals x minus three by the way, what is five squared? Don't you dare say ten calling? 25 But I'm hoping this this way you'll never do it on a test, right? If you have included when you make a mistake I'm not picking on you to make fun of you. I figure if I grind it. It's not going to happen when it counts. That's the whole goal And it's fun. I have to admit as well. I can't I can't deny that 28 yes And does 28 work in the original? Yep sure can right 55 For those of you who are screencasting at home. This is our 12th interruption. I apologize for the disjointedness of this But people keep coming in Driving me crazy 55 this looks pretty good Pat you asked 55? Yes. Now the good news is um They gave me the equation which probably means I really don't need to know the physics behind this You look passing. I'm not gonna freak out. I'm gonna read this carefully. I'm gonna say base e Yes, okay What do you think the letter p stands for? Probably pressure Pressure which is measured in what by the way Pascal all I'm saying is if I see a number that has a kilo pascals next to it. I'm putting that in the letter p Okay, uh, what does the letter a stand for according to this question? Okay, so if I see a number that has the kilometers next to it that's going in for the a They want me to find what? Oh, so they're asking me to solve for p What's that five? Okay, p is going to be 100 times e And then I'll show you what you would type on your calculator to the power of bracket negative 0.139 times Five And I'll show you what this would look like then This is nice. I'm not actually having to do l in effect this question. You know, it's really testing Do you know where the e button is on your calculator? That's what it tasks Because I have I'm not doing l n or anything like that. It's going to look like this 100 Do you know where the e button is on your calculator? Where You know where the you know where the lm button is on your calculator. It's second function lm See it there Because that actually types e to the power of bracket, which is way shorter to hit So I'm going to go times second function lm e to the power of bracket negative 0.139 Times five and the correct answer is looks like 49.9. Is that an answer there? I hope I think I hope I think I hope 50 50 Apparently five kilometers above the earth. It's 50 kilopascals By the way, what's the pressure at the surface of the earth? What's the initial amount? Read the question carefully What's sitting where the initial amount variable is 100 yeah pressure on seal up. It's actually 101 kilopascals if I recall 101 point something but 100 roughly Right, you can get a lot of information from these equations just by remembering I know what these variables mean even if I don't know what they are Right Bracket Try again I'll leave that up there for you Back, you know what I'll do. I'll go clear. I'll go second function enter I'll hit enter and then I'll get really really clever for you pat I'm going to go like this Clip I'll put the calculator in there too just for you And now you know what the heck I type next Yep, jimmy 58 love to oh an if then question Okay So again, I'll try and walk you through how my devious little brain works when I approach these A first thing jimmy I would look for is there a base change? Well, no both logs are base temp Okay, then if there's more than one log, I'd combine them if there's one log. I'll break it up I think they gave me one log. So I'm going to try and break this up What's happening jimmy between the 10 and the c-squared mathematically adding subtracting multiplying or dividing Multiplying what's multiplying inside a log the same as Adding right it's going to be this kiddo But you know what instead of writing c-squared can I just move the two to the front right away? Because we've been doing that a whole bunch of times Okay, um What is the log of 10? one because it's log base 10 up 10 plus two Sorry, colin. What did you say log c was are you saying this is one plus two times three? Seven this would be totally fair game on a non-calc section All right, you know what by the way on the provincial what they also do is So they have 16 I think non-calc questions But in the next 10 questions about eight of those can be done without a calculator as well Because that way kids that finished part one early aren't just flipping their thumbs. They can keep moving on But I'll talk about that when we get to june seven Someone else had one. I thought I heard seven zero If the answer is a isn't it Geez, I mean you can do that fast, mister. You get good at this after a while Okay Fly bothering you. Oh, there ain't no flies on me. Um positives on Top negatives on the in other words when I break this up What's on top is going to be positive what's on the bottom is going to be negative And I'm pretty sure I'm going to have to break this up because I got nothing else to work with here So I would write this as the log of x take away the log of 100 Take away the log of y again. The y is negative, but this time thing down there. Yeah, but it's dividing the x It's it's negative Pat, what's the log 100? What's the log of 100? 10 to what power equals 100? Right I see my answer. So I'm quitting I don't know either, but I've long stopped trying to figure you out. Yes, jen 56 I tried for a while there. I wasn't sleeping. It is ugly 56 Yeah Great question. This is nasty. Okay. I don't know. Let's find out Well, I'm can I I'll rephrase that jen it's scary looking 56 Okay, because here's what I think they've done They probably had the same number sitting there and there initially And then they said, ah, this exam's too easy. How do we make this tougher? And they probably took this question and replaced the number with a variable knowing that's going to scare kids But I think these are both base a in disguise. Are they not? So let's try writing it that way if I wanted to write square root as an exponent What would I write? So this is going to be a To the one half To the 6x minus 2 and that equals a squared To the 2x plus 3 Now what I I think I'm going to go power to a power on both sides I think I'm going to go like that And like because that's what I would do if it's like a five and a five there All right So I'll get this a to the what's half of 6x 3x Minus what's half of 2 half of 2 Half of 2. Thank you Multiplying by a half same as going half of Okay, uh that equals a to the I think we're going to get 4x plus 6 Yep, are my bases the same? I can equate the exponents now that means by the way, you notice I didn't do logs to solve this This also would be a fair game non-calc trickier non-calc, but non-calc question The equation you're going to end up solving is going to be 3x minus 1 equals 4x plus 6 Are you okay with the rest of it? I think you'll minus 3x from both sides and I think you'll minus 6 from both sides I think it's going to get negative 7a. I think but are you okay with the rest of it, Jim? Yep. Yes 83 I have no idea. You have to actually say hey, mr. Do it. I'd like you to look at number 83. I know you think I have these memorized, but I haven't yet If there was 105 questions instead of 110 then I probably have to memorize but it's those extra five questions Yep. Yep Totally it's base two base two colon two four eight 16 32 in fact, I'm comfortable asking a deal with a 64 or 128 or a 256. I'm comfy with all those And then it goes 512 1024 4,000 and sorry what if I'm going to put a big exponent. It's going to be a two to the Thank you. I would feel totally comfortable putting it there I don't know. I haven't memorized the test. I typed it up about a week ago. Okay Yeah It's counting by twos colon I'm not going to deal with three to the fourth. I probably would expect I think that was one of the ones I told you to memorize 81 Oh, yeah, I gave you a list of exponents that I said we're fair game, didn't I? Oh, yeah, yeah, I told me to write that down. Oh, look at that. Mr. Do if you think of these things in there done that Take care Oh, so when I said memorize them and I wrote down worth memorizing and then when I publish it in the notes online As stuff worth memorizing. I wasn't clear enough. Okay, my bad Apparently I have to be really obvious for calling Are you are you saying that by making the quizzes and making the review tougher? You actually did find the test better Really? Well, that's a good way to learn, isn't it? Why not find the tests easy for a change and find the homework tough That should be the way of courses run, isn't it? Really? Wow So that that's the goal It's not a pleasant procedure, but the test becomes much nicer. That's unit one. That's what we're going to be doing this next unit Yeah, we are What's my website calling? Click here to access notes Doesn't matter whether you're block e or f or g. I put it on all of them and I bet you it's called something like Worth memorizing. I'll bet you I'll bet you I'll bet you let's see. Is that it? I wonder I wonder I wonder Let's find out I'll put it on the desktop because I don't want to leave it there I'm using google chrome. It automatically does it without saving. Well, no, it takes up less memory and it's faster Oh, look at that. I see some exponents written in different colors. Look at that I don't know. There's probably other stuff. I've said worth memorizing along the way But that's the only lesson that I entitled worth memorizing Next surely you must have questions since you just got here You're doing good. Okay Cool enough anyone else For those of you listening at home people are thinking and humming and hawing This tutorial may be shorter than I planned But I'll probably send out the email to my big unit review tutorial that I ran last year It's about an hour long If you feel like you need to see the entire unit all in one fell swoop I'll send an email out with that link For which one? 80 80 This this one is actually nasty. Did I do this one in class with you? I did it one of my blocks In fact, I would argue that number 80 I think it was one of the five toughest questions on this review Okay, and the reason is what they're asking They're asking how many times greater Will 50 weeks be than 20 weeks. Let me copy this first of all And to do that I need to put a couple of things together Jen suppose you have 50 dollars on you I have five dollars on me How many times more than me do you have? How do you get a 10 from a 50 and a five? Mathematically, how would you get a 10 from a 50 and a five? I 50 times five is 250. How would you get a 10 from a? Would you not go 50 divided by five? Okay, let's try it again because this is important. I'm making the point here Let's suppose you have a hundred bucks and I have 20 bucks How many times more than me do you have? How would you turn a hundred and a 20 into a five? divide I think here's what's going to happen. They want to know how many times bigger I think I'm going to find an algebraic expression for 50 weeks Find an algebraic expression for 20 weeks and divide them Let's see 20 weeks. Oh, and it's exponential growth. So I probably would have written this somewhere Did they tell me the final amount after 20 weeks? No, so I'll write a Did they tell me the initial amount? No, so I'll write a zero ooh Triple I'm pretty sure that means there's going to be a three here Triple every what how many weeks? That's my period Seven And I I think 20 weeks. That's where the 20 would go. That's an algebraic expression for how many insects there are after 20 weeks I'm going to do the same thing for 50 weeks I don't know the final amount still I don't know the initial amount still Triple 50 weeks every seven weeks I'll call this final amount for 20 final amount for 50 And to find out how many times bigger this guy is than that guy what mathematical operation. Am I going to do? Divide I'm going to divide this by that, but I'm not going to divide left side by left side I'm going to divide expression by expression. I'll write it as a big fraction It's going to look like this. Here's my 50 weeks Here's my 20 weeks And the first thing I notice I breathe a little sigh of relief because what happens to my initial amounts They cancel which is good because I didn't know it and I was looking at their answers going How the heck did they get numerical answers and tell me the initial amount? Well, the initial amount would be the same for both because it's the same insect colony Oh, that's going to cancel. In fact, here's what I have three To the 50 over seven divided by three To the 20 over seven Oh Are my bases the same? When I'm dividing what did I do with the exponents? Think carefully subtract Right, remember math nine. I think the final answer is going to be three to the power of 50 over seven take away 20 over seven And do you know what 50 over seven take away 20 over seven is I think 30 over seven I think it's going to be three To the 30 over seven then when you type this into your calculator You're going to go three to the power of bracket 30 divided by seven closed bracket. That should give you it 110.87 b Do you see why I mean felt felt this is fairly nasty first of all you have to put that connection of dividing together Then you're finding fascinating another interruption then you're Don't want you then you're finding an algebraic expression for 20 weeks And it's a little scary because you've got two things you don't know which terrifies kids makes them think they're doing it wrong 50 weeks two things you don't know terrifies kids makes them think you're doing it wrong Ah, but when you write this amount divided by that amount Stuff cancels and you get up with all numbers. Yep I would consider this fair game as a nasty question Are you asking me with 12 of these beyond the test? No Does that make sense though? Not I've gone through it. Yeah, okay I don't like the way this one's phrased very much either Um, this was number 80. Let me just look for a second I'm a little surprised. This was from the january 2004 exam. It was question number 20 I'm a little surprised on the january 2004 exam. There was one more log question I would have put this one as the last log question because I felt this one was fairly tough Usually when you come to a yucky one the next one is a new topic and real easy usually next 91 ooh near the end Good question. This one is totally fair game And in fact, there will be one something like this on the non calc section of your task Collin, what's my base on the left side and let me give you a hint. It's not one ninth Yep In fact three to the what? Okay, I'm going to write this three to the negative two to the power of x and yeah You're ready going one step ahead power to a power and I'm going to write this as 27 is three to what power Collin three to the third good for you. I'm so glad you got that right to the two minus x Can you see where we're going now? Okay. Yeah, you want to be really careful taking I love taking shortcuts I've made so many sloppy mistakes getting rid of those brackets that I usually don't hear on a test especially It's going to be yeah negative two x three to that power Equals three to the six minus three x Collin are my bases the same? Then I can equate the exponents in fact the equation. I'm going to solve is this puppy here I would plus three x to both. Holy smokes. I'm done because if I plus three x to both sides Won't I just get one x equals six got the x by itself already D. Oh, that was kind of nice People are good