Question

How come log5 25^4 reduces to 4 log5 25
then 4 times 2
then finally eight?

Answer 1

log x^n = n log x
so
log5 25^4 = 4 log5 25

25 = 5^2
so
4 log5 25 = 4 log5 5^2
= 4*2 log5 5

5^(log5 x) = x
5^(log5 5) = 5
so
log5 5 = 1
SO
4*2*1 = 8