Question

Expand the logarithm: log((s√7)/t^2)
I know the answer to this question is log(s)+1/2log7-2log(t) but i'd like to understand WHY that is the answer, not just the steps but also how to solve this kind of problem in the future

Answer 1

application of log rules

log(ab) = log(a) + log(b)

log (x^n) = n log(x) why??

x^n = xxxx....x, n times

log(xxx...x) = log(x) + log(x) + log(x) + ... +log(x) ; n times

Answer 2

a/b = ab^(-1)

log(a/b) = log(ab^(-1))
= log(a) + log(b^(-1))
= log(a) - log(b)

Answer 3

log(1) = log(a/a)
= log(a)-log(a)
= 0