SOLUTION: which of the following is the largest? A. {{{log(0.5,8^40)}}} B. {{{log(2,32^8)=x}}} C. {{{log(3,27^12)=x}}} D. {{{log(4,2^60)=x}}} thank you.

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: which of the following is the largest? A. {{{log(0.5,8^40)}}} B. {{{log(2,32^8)=x}}} C. {{{log(3,27^12)=x}}} D. {{{log(4,2^60)=x}}} thank you.      Log On


   

Question 1019573: which of the following is the largest?
A. log%280.5%2C8%5E40%29
B. log%282%2C32%5E8%29=x
C. log%283%2C27%5E12%29=x
D. log%284%2C2%5E60%29=x
thank you.
Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!
"What is the logarithm of a number to a given base?"

is the same question as
 
"To what power must the base be raised to get the number?"

That is:

log%28B%2CA%29=x is equivalent to B%5Ex=A


A. log%280.5%2C8%5E40%29

Set it equal to x:
log%280.5%2C8%5E40%29=x
0.5%5Ex=8%5E40
%281%2F2%29%5Ex=%282%5E3%29%5E40
1%2F2%5Ex=2%5E120
2%5E%28-x%29=2%5E120
-x+=+120
x=-120

B. log%282%2C32%5E8%29=x
2%5Ex=32%5E8
2%5Ex=%282%5E5%29%5E8
2%5Ex=2%5E40
x+=+40

C. log%283%2C27%5E12%29=x
3%5Ex=27%5E12
3%5Ex=%283%5E3%29%5E12
3%5Ex=3%5E36
x+=+36


D. log%284%2C2%5E60%29=x
4%5Ex=2%5E60
%282%5E2%29%5Ex=2%5E60
2%5E%282x%29=2%5E60
2x+=+60
x=30

Which is largest?

Edwin