Question 1019573
<pre>
"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(B,A)=x}}} is equivalent to {{{B^x=A}}}


A. {{{log(0.5,8^40)}}}

Set it equal to x:
{{{log(0.5,8^40)=x}}}
{{{0.5^x=8^40}}}
{{{(1/2)^x=(2^3)^40}}}
{{{1/2^x=2^120}}}
{{{2^(-x)=2^120}}}
{{{-x = 120}}}
{{{x=-120}}}

B. {{{log(2,32^8)=x}}}
{{{2^x=32^8}}}
{{{2^x=(2^5)^8}}}
{{{2^x=2^40}}}
{{{x = 40}}}

C. {{{log(3,27^12)=x}}}
{{{3^x=27^12}}}
{{{3^x=(3^3)^12}}}
{{{3^x=3^36}}}
{{{x = 36}}}


D. {{{log(4,2^60)=x}}}
{{{4^x=2^60}}}
{{{(2^2)^x=2^60}}}
{{{2^(2x)=2^60}}}
{{{2x = 60}}}
{{{x=30}}}

Which is largest?

Edwin</pre>