Log25 - log125+1/2 log 6252 over 3 log5

Question

The question says evaluate

Answer 1

I read this as:

(log(25)-log(125)+½log(625²))/(3log(5)).

25=5², so log(25)=2log(5); 125=5³, so log(125)=3log(5); 625=5⁴, so log(625)=4log(5) and log(625²)=2log(625)=8log(5).

The problem can be rewritten:

(2log(5)-3log(5)+4log(5))/(3log(5))=3log(5)/(3log(5))=1.

So the solution is 1.