Properties of Logarithms - Part 2 - Solving Logarithmic Equations

[JonibekShaxXx]

what is ln???? 2lnx+ln(x-1)+ln4 and i got x=3, is it correct ?

[GenBLiTz]

I don't get the 2nd part of the cancellation law :(

[flamerFox]

Natural born teacher.

[lolguz]

buy a white board, much better financially and ecologically

[patrickJMT]

@lolguz no

[kikbxr94]

ty, but i dont understand why did u divide by 2? can you do that? i thought you cant and you had to raise the 2 as a power so Lnx^2 = 1. Ty

[bryfryable]

wait, in the first problem why dont you take the number 2 and turn it into an exponent? to make it ln x square= 1

[superflier0112]

I FUCKING LOVE YOU! YOU SMART SON OF A BITCH!!! I BOW TO YOUR GENIUS!!!! THANK YOU!

[Shineinpoverty]

i like that you write ln as log base e. for some reason ln confuses me.so that helps

[ebenygraves]

thank you for doing these videos. i got an excellent grade in prealgebra, and now working with college algebra. thank you so much for helping us with a difficult subject. glad you are doing it. i'd be lost otherwise!

[karenjimenez]

i truly do appreciate your help thanks!!

[ddclarkson]

You Rock!!!!

[Gabe1794]

te amo

[ilovemysunshine09]

still a bit confused but i can easily watch this video till i get it, thanks!!

[patrickJMT]

@ilovemysunshine09 yes, i rarely got stuff the first time around!

[sarazuu]

why do you use natural logarithms, why not only logarithms?

[Alphilles3922]

@sarazuu I know I'm not Patrick but he said (at one point or the other, either in this video or the first one) that it tends to be generally easier. I think it's because the exponential function, e, tends to show up quite a bit so if it ever shows up with the natural logarithm, you can always simplify it to 1 to make whatever you're doing easier. Hope I helped :')

[pianoplayindrummer33]

You sir, are amazing

[patrickJMT]

@pianoplayindrummer33 thank ya : )

[archerb88]

how to solve log (n+9)=log 4n

[patrickJMT]

@archerb88 n + 9 = 4n, and check your solutions

[h4xmode]

I don't even have to go to school anymore.

[avalanch08]

Just learned a 2 week lesson in 19 minutes... Damn test tomorrow too lol

[knotnyce]

patrickJMT or die :D 

[spe3d3]

thx due, was really helpful keep doing what u do :]

[famedusma96]

help! i'm nosebleeding here! :(

[famedusma96]

best online math teacher ever! you have a gift of teaching.. God bless you!

[animelovergal2002]

I can't remember ever doing logarithms in high-school (the teacher would start from Ch. 2 and by the end of the year, we'll be at just chapter 12.5 and the log, sin, tan, cos amd functions would be in the next few chapters.

Your a great teacher,any subject in Math I have problems with, I always end up watching your videos

[cpfullback]

lol i wish i had seen this video before i took my final exam.

[cfonangel]

u are my favorite teacher on YouTube :)

[dragooner4]

wait could u simplify the log so like

2ln(x)=1

>ln(x^2)=1

e^1=x^2

x=sqrt(e)

or am i just making it more complicated

[0nDeck]

this makes me want to cry .

[BrownFlip7852]

i hope you're getting paid for this because you definitely deserve it

[mrhoppy654]

Ooh, a lefty. :D

[cballet315]

thanks dude

[Aquateen1984]

Thank you, you have helped me immensely in pre calc

[BecaMae]

brilliant

[jonathanokoro35]

how to solve xe^(2x)-2=2

I got this on a quiz and I don't know how to solve it.

[newyorkcitynewyork19]

Nicest handwriting for a lefty!

[tibor29]

Damn it I'm having harder time understanding logarithms than advanced calculus...

[FilmEngineer]

You're killing so many trees with your videos. Why don't you just use tree sap as ink.

[9112001ification]

Fuck logarithms, they are bullshit. whoever created logarithms thought it would be awesome to mix around a bunch of numbers, god damn your soul.

[suki29168]

still dont get it =[

[yeijie456]

Thanks Patrick...My Algebra 2 teacher is shit...expects us to understand logs with just 5 examples without the properties....

[ngyngxn]

I used calculator to get x for the last question = 1.688305458 or -2.188305458 , seems ln(negative) is incorrrect , should x be 1.688305458 only when we solve it?

[AsianWitAttitude]

OMG TY SO MUCH SAT IS TOMORROW AND THIS HELPED ALOT.....lol :)

[filthsauce]

the value of having a teacher you can rewind is unbelievable

[patrickJMT]

@filthsauce yes, i think it really is a good method of learning material - your own 'personal' teacher

[MysTeri0usMatT7]

@patrickJMT 7:20, instead of solving that quadratic equation using the quadratic formula, could you just go on and use e=mc2 to solve?

[2GXCVT]

@MysTeri0usMatT7

I hope nobody reads that and takes you seriously :P

[happychobits]

OMG, y u so amazing? :D thank you!

[lolkiwi]

This is so helpful. Thank you so much!

I hate logs! lol

[pyrobotnic]

HOLY CRAP!!! thank you so much, the only thing that I get confused in class with is ln and log base of e! you're a life saver. bring it on math final!

[DangerousPirate]

You should move your stack of paper to the side and replace them with a reusable cardboard platform so that it won't ruin your table nor waste paper.

[patrickJMT]

@DangerousPirate my table is fine and this is not a waste of paper. it is probably one of the most useful uses a piece of paper can have.

[unspoken314]

@patrickJMT i think what DangerousPirate means is that you're wasting paper when the permanent marker bleeds through to the next sheet. if you put a piece of cardboard under the piece of paper you are using, it can bleed onto that and not onto the next sheet of paper, therefore saving paper.

[unspoken314]

@patrickJMT i think what DangerousPirate means is that you're wasting paper when the permanent marker bleeds through to the next sheet. if you put a piece of cardboard under the piece of paper you are using, it can bleed onto that and not onto the next sheet of paper, therefore saving paper.

[meljeanli8888]

@patrickJMT A whiteboard would even be more useful. And more "green"...but I see you're already using one in your newer videos

[patrickJMT]

@meljeanli8888 no, i am back to paper.

[cboseak]

@DangerousPirate an economist would say "cost of paper<cost of new table=keep using paper" so really there's nothing wrong with using paper and throwing out the excess used to prevent bleeding based on "MC<MB"

[THomasSnipes1181]

How many people watch these videos every time you do your homework?? I know i do, even if i know what i am doing you make me feel more confident with math, for that i could not thank you enough!! Your amazing Patrick keep it up!

[patrickJMT]

@THomasSnipes1181 glad that the videos are helping : )

[THomasSnipes1181]

You have no idea how much easier you make my life. Thank you so much!! I watch your videos every time i do my homework, even if i know what i am doing, you always seem to make it more and more clear. God bless you..

[Swaginrags]

I FUCKING LOVE YOU!!!!!

OMFG I JUST MIGHT PASS TOMORROW HOLY SHIT!!

[Swaginrags]

I FUCKING LOVE YOU!!!!!!!!!!!!!!!

OMFG I JUST MIGHT PASS TOMORROW HOLY SHIT!!

[AudioAnime]

The 15 people who disliked wished they had found this video before their math test.

[ASAGAMA1]

In the last example we must reject the negative solution. Great job!

[shimhq]

thnx to u i passed my test, ur services are really appreciated :)

[nikkk7]

OMG THANK YOU MY TEACHER SUCKSS

[iluvcoOki3s518]

why can't YOU be my teacher... wait you are <3

[fruitsbasketloveable]

what do you do with equations like: ln (4x-9) = ln x

and 2+ log3 2x= -3 ????

[AZZAflipnote]

it doesnt cancel they simplify i think

[yodudo154]

finals TOM! you have no idea how much you helped =D

[moneysuccesslegacy]

This area of Algebra is mentally raping me

[satfreegames]

your a life saver

thanks alot

i liked

commentd

subsribed :)

[RoxStar09]

Lifesaver!! =D

[lexiloulouu]

you answered a question i wasnt even looking for yet

thanks

[emmacxoxo1]

this was super helpful ! my teacher doesnt sufficienly explain how to do problems in class, and we're forced to look elsewhere...thank u soo much for putting up these video's and saving my pre calc grade :D<3 theyre really informative

[Nospherith]

i f'in love you so much dude

[zxBOYERxz]

I just thought i should tell you that your a boss! i have a math test tomorow and i only understood like half the stuff, but thanks to you i might just pass algebra 2. Muchas Gracias amigo!

[patrickJMT]

@zxBOYERxz i hope the test went well

[AZZAflipnote]

@zxBOYERxz did you pass Spanish too?

[zxBOYERxz]

@AZZAflipnote yeah i got like an A....don't remember any of it now though :p

[thej0ker09]

YOU.........ARE..........GOD

[lemartzky123]

sorry i dont have speakers here so i cant here u explaining

[lemartzky123]

and log_e(7) into ln 7?

[lemartzky123]

log_e^x=1/2 turn into 2:16 ?

[Seattle206723]

You know what I am at the end of 98 math and not one time has my book or the damn teacher showed me this method. My God people. Thank you patrickJMT..

[EREX94]

THANK YOU!^infinite :)

[MissMiaShaw]

I love you? :)

[videoK1]

Dude you fucking taught it wrong and made me fail.

Jk, thanks for the help.

[njtxconnect]

Thankyou...you helped me through the whole semester of college algebra :)

[Jesskamorerless]

Sir, thank you so very,very much. I am a visual learner and my algebra/trig teacher expects us to just know how to work problems out with the properties. YOU ARE AWESOME. Subscribing.

[AlienRelics]

That was a bit confusing, I'm listening at work as I can't watch it nonstop. Your words said "e to the e is e" but you wrote "e to the e is x".

Keeps me on my toes! Thanks for the videos.

[kidduelists]

dude how are you

[tudah3]

ok. you're too cool!!

[yoyo5411]

i cant figure out how to solve for x, when the base of the logs are different, such as log_5(x-1)=log_7(x)

[Gnomepaste]

Could you do a video on Vertical stretches and compressions of logarithmic graphs? please? y=a*logbX

[luxemkingII]

what if you multiply a logarithm with another log?

because I have this problem:

log a (b)* log b (a) =x

the question was if x=1 or x=ln ab or x=loga+b (ab) or x=log a+b (a) + log a+b (b)

or x=ab

[dajakesta1234]

ur da best

[junk3m0]

you're the best math teacher ever!!!!!!!!!!!!

[yurhomezjonez]

wow your a great teacher! all my teacher does is stand at the front of the classroom and solve problems in front of us without fulling describing how to do it. he didn't even tell us all of the laws of logarithms. the funny part is that he's been teaching for like 30 years. all those poor students!

[MessiLionel1010]

@patrickJMT You are amazing at teaching I wish you were my teacher!!

He sux!!

[patrickJMT]

@MessiLionel1010 just keep watching and i will be!

[liverbird66]

I fucking hate logarithms

[patrickJMT]

@liverbird66 What sound does a tree make if you hit it with a drumstick? A logarithm.

[redthreaddreams4]

@patrickJMT ha ha ha thats pretty funny :) LOL I had to think about that :) GREAT JOB MAN!

[Str33tFiGhTeR1]

@patrickJMT lol nerd talk. I love it!

[rocknrog33]

@patrickJMT lol nerdiest math pun I've every heard :)

[narrowonflow]

@patrickJMT the reason y u r such a good teacher is because u r not jst a mathematician ur a philosopher !

[jaredpistoia]

@patrickJMT i am a drummer . . . this is great. ha

[knotnyce]

@patrickJMT  or die XD

[kwaziedreamer]

@liverbird66 I wish I could like this comment a thousand times!

[mskochergirl]

@liverbird66 lol.. couldnt have said it better myself

[routercpu]

I love math but then sometimes, it's really hard to solve complex problems.

[PatrickAndHisLSD]

Love how your a lefty dude, lefty pride!... and your name is patrick... and your teaching is the greatest! very nice 

[patrickJMT]

@PatrickAndHisLSD yes, but where is my lsd? i did just buy a san pedro cactus... now just gotta wait for it to grow bigger!

[Superblockman]

Groovy man, thanks

[GoodCoffeeInc]

I owe you my passing math grade.

[Tmytate]

Awesome videos Mr.Patrick.....I just started Pure Mathematics Unit 1 and this is my second topic and really needed some clarification in terms of the various laws of Logarithm and I must say you're such a help! Thanks a lot! Keep up the good work! :)

[Bartney1994]

Thanks!

[Negronigganigga]

you understand that youre a fantastic teacher I hope

[patrickJMT]

@Negronigganigga i do what i can. thanks for the kind words.

[inuyasha112211]

@patrickJMT

hey Patrick thanks for the video iam going to be doing logs soon, i watched your videos, i think i understand it

l

[Bankaiboi47]

Once again, this is really great! I had to refresh my mind on logs again. You may not be a professor(reading other comments), but are you a teacher? You teach it so simply. Because teachers can teach, not professors, their not technical certified teachers. My professor is foreign, so i dont know what he says most the time :/ Thanks Again though!

[raliku100]

great video..what's missing is the connection between inverse functions and natural log functions..please update if u have time. thanks

[finalshineag]

Awesome Professor. PatrickJMT. Your videos really help. Hope you post more Cal II stuff.

[patrickJMT]

@finalshineag thanks! although i am not a professor (that is an earned title by teaching at a university!). let me know what else you want to see... i have lots of calc 2 stuff at this point, but let me know what is missing

[archnoriega]

Thanks for being very cool and teaching out of your own time! You Rock!

[patrickJMT]

@archnoriega just doin' what i can

[folezicle]

Cheers mate.. Youtube used to be a place which made me procrastinate and waste time, instead of learning maths..

Now Youtubes a place that gets me an A+ in a log test :D

[patrickJMT]

@folezicle now you can waste time and learn : )

[like9orphanz]

im in calculus and my final is right around the corner and realized i forgot all about these haha

[cutekitten12]

lol nice drawing at the end, and these vids are great!

[patrickJMT]

@cutekitten12 heheeh thanks!

[wakefan63]

So, whenever you don't have the log or ln already in the equation, do you put them on both sides.

[olev456]

i started to like and understand math again :D

[nauticasplash]

Hey! Thanks for this great video! Can you help me with this question? (lg 24)(lg x²) = 5 lg 12

[krishna1254]

hmm..

awesome work i was nt able to understand log frm last 2 years so nicely ,dat i hve undrstand in 9 min..

lubes u..

really..

[MsTwilight55]

HUH?

[marshmelowmat]

technically you did make a mistake in the quadratic. You said that the two negatives become a positive, but e is squared so it becomes a positive (PEMDAS), meaning that you are multiplying a negative by two positives to get a negative answer.

1-4(2)(-e^2) = 1-8e^2

but thats not what the video is all about, so everyone can stop arguing.

[mhm776]

dude what are u tripping. e is just a constant. That is all! :D Patrick did it correctly.

[jaime1894]

Dude, you got you Quadratic formula wrong, hahaha it -b plus or minus the square root of b^2 -4(a)(c) all of this divided by two. hahaha

[gilkesk]

@jaime1894 thats mean.

we all make mistakes

[phjl12]

@gilkesk Ironically so did this guy.. you divide it by 2a not just 2

[gilkesk]

@phjl12

true true!

salam brother

/watch?v=u4hJ1W0yGk8

[SuperBill1982]

@jaime1894

2 negatives multiply what happens?

[whisper012]

@jaime1894 he's not wrong, he explains how the - turns into a positive because it's multiplyed by another - ... you have to pay attention before your allowed to be a smartass mate.

[brownskinnedgurl1]

u make this look so easy. Thank you!!

[BEARINTUTU]

4:28---wont the cancelation property just cancel out the (ln)s alone, so without all that work u can see, its x = 1? because e is a number, so e cant stay raised to e, it would be 1, right?

[alakazamfan123]

This is going to help me in my upcoming higher mathematics test.

[sullivanseven]

At 5:25 is it the sky and stars? if so why is the sky white? :)

[love2huntak]

Awesome videos, very helpful :)

[diorfashion23194]

in response to dyoung1843

actually i took the ab calc test last year and I scored a five on my ap exam

i worked my butt off for the grades and that score and this video did not help me alone

i did a lot of independent study and late hours hitting the books and studying at library but it fortunately paid off for me

[akvino]

Good video - I did this 15 years ago, and it is nice reminder when you need it again.

Got to know math if you're programming!

[sirlepto]

Now it looks so easy XP

[nicoargca]

why naturals!! I'm dealing with common ones!

[TheFanofFPS]

I wish you were my Algebra 2 honors teacher. My teacher doesn't even know what she's doing.

[diorfashion23194]

thanks so much patrick for posting this video

you helped me ace my ab calc test!

thank you

[dyoung1843]

dude i took the ab calc test and this is way way way easy stuff compared to that if you didn't know this idt you aced the ab calc test dont believe it at all

[lol18ization]

For the problem ln(2x +1) = 2 - ln x, [ -1 - √(1 + 8e²) ] / 4 is not a solution since x cannot be negative, as you cannot raise a number to a power to obtain a negative one. So the answer is only the positive value.

[aquapendulum]

Above: The kind of trap that is usually set up in final exams (during my high school year - 2004, at least). Protip: Don't fall for it.

[stellarXbell]

this is amazing. i should have watched this vid before i took my log test. you rule.

[TheSuperstardude]

i love u patrick. u r the best teacher in the world.

[theboywhogotlost]

Awesome thanks for the help!!! ur an invaluable teacher!!!

[liliannx3]

Why couldn't you just be my functions teacher :|

I wouldn't be failing.

[havugaimana]

could you pliz solve this one for me

finding the inverse of f(x)=ln(2+lnx)

[lafpohl]

Saw the article in the statesman. What an AWESOME service you are providing. I thank you, as a mother and teacher. FYI, there is an tutor in Austin, tx, that charges and gets $175 an hour for high school math tutoring. I'm shocked but people pay it.

[beerndumplings]

haha nice stick figures at the end.

[MiSTAAAHMEK]

in the quadratic equation isn't it 4(2)(-e^2)?

[burnerj2000]

hey do you have a video very similar to this one but instead of using e and showing how e cancels out. is there one with numbers like 2^3-z= 625

[burnerj2000]

i love u thx a bunch !!!!!!!!!!!! it gave me a headache trying to understand my dumb book ur better

[scout6686]

i'm' such a prostiute

Now I don't have to read my math test book anymore! Woohoo. I hope you have other videos on more pre-calc. topics. lol