Question

Im not sure how those two equal eachother, help?

Answer 1

`(\log_5 9)/( \log_5 25)\\\\\\=(1)/(\log_5 25) \log_5 9\\\\\\=(1)/( \log_5 5^2) \log_5 9\\\\\\=(1)/(2 \log_5 5) \log_5 9~~~~~~~~~;[\log_a m^n =n \log_a m]\\ \\\\=\frac 1{2} \log_5 9~~~~~~~~~~~~~~~~;[ \log_a a = 1]`

Answer 2

Yes.

Explanation:

`\sf (log_5 \ 9)/(log_5 \ 25)=(log_5 \ 9)/(log_5 \ 5^2)`

`\boxed{log \ a^m=m*log \ a}`

`\sf =(log_5 \ 9)/(2*log_5 \ 5)\\\\ \boxed{Log_a \ a = 1}\\ = (log_5 \ 9 )/(2*1)\\\\=(1)/(2)log_5 \ 9`