Computing the first digit of the logarithm in base 10 is easy. log(23456) = 4.???, because 10^4 <= 23456 < 10^5.
The first digit of log in base 10 of (x^10) is the SECOND digit of log in base 10 of x.
All you need to do is raise the number to the 10th power and read off the first digit of its logarithm -- d. Then divide by 10^d to reset the decimal point to the right of the leftmost digit, and continue.
Check out the paper "Computing logarithms digit-by-digit" for a full explanation.
@gmayer66 For example: log(3) = 0.???, so the first digit of log(3) is 0. 3^10 = 59049. log(59049) = 4.???, so 4 is the second digit of log(3). 59049/10^4 = 5.9049. 5.9049^10 = 51537752.07 log(51537752.07) = 7.???, so 7 is the third digit of log(3). 51537752.07 / 10^7 = 5.153775207 5.153775207^10 = 13220708.19 log(13220708.19) = 7.???, so 7 is the fourth digit of log(3) So log(3) = 0.477...
The 10th power of 5.789362 has 8 digits with a log10 between 7 and 8. Dividing it by 10e7 helps us to split the 0.7 from the rest of the result. The remaining number is raised again to the 10th power, this time a 7 digit number with a log10 between 6 and 7. Dividing it by 10e6 and adding the 6 to the 7 helps us to split the 0.76 from the rest of the result. The remaining number is raised again to the 10th power, this time a 3 digit number with a log10 between 2 and 3, now we got 0.762.........
grt stuff....made it easier for me...thanks a lot.
ashwinxxl 2 months ago
thumbs up if you went check if it was rigth
domfalcolioni 8 months ago
This has been flagged as spam show
I like the song(-)(:)
thenochistlense 11 months ago
it will take less time by logarithm table
vivek1471990 1 year ago
whaaaaaaaat??????????????
aparajita1194 1 year ago
Computing the first digit of the logarithm in base 10 is easy. log(23456) = 4.???, because 10^4 <= 23456 < 10^5.
The first digit of log in base 10 of (x^10) is the SECOND digit of log in base 10 of x.
All you need to do is raise the number to the 10th power and read off the first digit of its logarithm -- d. Then divide by 10^d to reset the decimal point to the right of the leftmost digit, and continue.
Check out the paper "Computing logarithms digit-by-digit" for a full explanation.
gmayer66 1 year ago
gmayer66 1 year ago
Nice...lol i dont get it... i rather use scientific calculator
Sham2951 2 years ago
wow.....lets smoke some pot to this music while were at it...
XxTONYDAGUNxX 2 years ago
Huh? hahahah...
kala203 2 years ago
gud stuff man....
Arsi823 2 years ago
not smart...someone taught him or her how to do it...then shear arrogance takes over...
don't assume people know what you mean
nothing goes without saying when it comes to teaching....if you can't humble yourself....don't bother post anything intellectual
EyonDreams 2 years ago
Don't get it. You should spoke so we know what you're talking about.
aegisforex 2 years ago 2
holy sh*t maaaan!!!
Trackman2007 2 years ago
What is that music? It's pretty funny. It sounds like the demo for some old keyboard...
JohnZartman 3 years ago
It's an old thai song named "ํYuan Ya Le" (ยวนย่าเหล) played on an old keyboard.
Pomzazed 2 years ago
amazing
RyaZila24 3 years ago
lol omg i dont get it.. O__O you guys are crazy smart..
ilyforever023 3 years ago 4
The 10th power of 5.789362 has 8 digits with a log10 between 7 and 8. Dividing it by 10e7 helps us to split the 0.7 from the rest of the result. The remaining number is raised again to the 10th power, this time a 7 digit number with a log10 between 6 and 7. Dividing it by 10e6 and adding the 6 to the 7 helps us to split the 0.76 from the rest of the result. The remaining number is raised again to the 10th power, this time a 3 digit number with a log10 between 2 and 3, now we got 0.762.........
Gerald56 3 years ago 2
Very clever and innovative! It is also helping people to grasp the concept of logarithms. [* * * * *]
Gerald56 3 years ago
ugh
bob1012112 4 years ago