Marvin earns $8.25 per hour at his summer job he wants to buy video game system that costs $206.25 wright equation to model the relationship between number of hours worked h and amount earned e

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.