Which of the following is equivalent to log32^4?

the answer is C ...

The trick to evaluating this expression lies in writing both 32 and 4 as powers of 2:

log to the base 32 of 4 can be re-written as:

y = log to the base 2^5 of 2^2 (Because 32 = 2^5 and 2^2 = 4.)

Now convert this logarithmic statement to an exponential one. To do this, write:

y log to the base 2^5 of 2^2

2^5 = 2^2

5y

2 = 2^2 Note that both sides are to the base 2.

THus, 5y must equal 2, so that y comes out to y = 2/5, or 0.4.

I have had to make assumptions here: I reworded your question to"Which of the following is equivalent to log to the base 32 of 4?" NOT equivalent to log32^4.