If $\log_{30}3=a,\log_{30}5=b$ then show what $\log_{30}8$ is

Question

If $\log_{30}3=a,\log_{30}5=b$ then show what $\log_{30}8$ is.

I am having trouble trying to get 8 to be some sequence with 5,30,3. Any hints?

Answer 1

$ \log_{30}8=\log_{30}2^3=3\log_{30}2=3\log_{30}\frac{30}{5\ast3}$

$3\log_{30}30-(3\log_{30}5+3\log_{30}3)=3-3b-3a=3(1-b-a)$