A logarithm expression always asks a question about an exponent.

That is, the logarithm expression

logB(A)  

asks this question:

Question:  "What exponent must we assign to the base B that will give A?"

If we can answer that question, the answer is what logB(A) equals. 



---------------------------

 log5(625)

That asks the question:

Question: "What exponent must we assign to the base 5 that will give 625?" 

Let's find out the answer to that question by breaking down 625:

625 = 5×125 = 5×5×25 = 5×5×5×5 = 54

So the answer to the question is 

Answer: "We must raise 5 to the 4th power to get 625."

Therefore, 

log5(625) = 4 

Edwin