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.