Question

Hi! So I'm asked to simplify logs:

log(base 3)X+5log(base1/3)X

I have no idea how to simplify with different bases. Is it even possible?

Answer 1

Yes it is possible

Answer 2

\[\log_ab=\frac{\log b}{\log a}\]

Answer 3

log(base 3)X+5log(base1/3)X
= log(base 3)X+5log(base3)X/log(base3)(1/3)

Answer 4

You can do it now?

Answer 5

I thought it would be log X/ log 1/3 if I used that property? Since A=1/3 and B=X

Answer 6

Well base 10 is just the same as any base, and sorry I should modify my formula:

Answer 7

\[\log_ab=\frac{\log_nb}{\log_na}\]

Answer 8

I'm confused as to why it would be 5log(BASE 3)X/log(BASE 3)X like how is it that instead of 10 it would be 3 for the base

Answer 9

Well I put n=3