SOLUTION: Evaluate the logarithmic expression. Do not round the expression until the final answer. When necessary, round to the nearest hundredth. log[2]32 (1/5)

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Question 627858: Evaluate the logarithmic expression. Do not round the expression until the final answer. When necessary, round to the nearest hundredth.
log[2]32 (1/5)
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
log%282%2C+%2832%5E%281%2F5%29%29%29
This expression is simple to evaluate if you understand what logarithms are and if you can figure out powers of 2. A base 2 logarithm, like yours, is an exponent that you would put one a 2. This particular logarithm is the exponent you would put on a 2 to get 32%5E%281%2F5%29 as a result.

So what power of 2 does result in 32%5E%281%2F5%29? The answer is easier than you think because 32 happens to be a power of 2! 32+=+2%5E5. Substituting this into your expression we get:
log%282%2C+%28%282%5E5%29%5E%281%2F5%29%29%29
Using our exponent rule for powers of a power (i.e. multiply the exponents) we get:
log%282%2C+%282%29%29
Now it is easy to see what power of 2 (the 2 in the base) results in a 2 (the 2 in the argument). It is 1! So:
log%282%2C+%2832%5E%281%2F5%29%29%29+=+1