Question 21112
The question is: To what power (that's x) should 32 be raised to equal 1/8?

You can use logarithms to solve this.

{{{32^x = 1/8}}} Take the log of both sides.
{{{xlog32 = log(1/8)}}} Divide both sides by log32
{{{x = (log(1/8))/log32}}} Use your calculator to find the logarithms.
{{{x = -0.6}}}

Check:

{{{32^(-0.6) = 0.125}}}
{{{0.125 = 1/8}}} 

If you not into logarithms yet, try this:

{{{32^x = 1/8}}}  Now {{{32 = 2^5}}} and {{{1/8 = 2^(-3)}}}
So you can write:
{{{2^(5x) = 2^(-3)}}} Since the bases (2) are equal, the exponents must be equal.
So we have:
{{{5x = -3}}} Divide both sides by 5.
{{{x = -3/5}}}
{{{x = -0.6}}}