Rewriting $(\log_{11}5)/(\log_{11} 15)$

Question

I'm struggling with this can anyone tell me the solution of this?

$$ \frac{\log_{11}{5}}{\log_{11}{15}} $$

A) $\log_{11}{15}$

B) $\log_{11}{5}$

C) $\log_{5}{15}$

D) $\log_{15}{5}$

Answer 1

$$\frac{Log_ca}{Log_cb}=Log_ba$$ $$\frac{Log_{11}5}{Log_{11}{15}}=Log_{15}{5}$$

Answer 2

Hint. You have $$ \log_{11}5=\frac{\log 5}{\log 11},\quad \log_{11}{15}=\frac{\log 15}{\log 11}. $$

Answer 3

note that $$\log_{15} 5=\frac{\log_a 5}{\log_a 15}$$ where $a>0$ and $a\ne 1$

Answer 4

Have you ever seen the change of base formula for logarithms before: $\log_{a}{b}=\frac{\log_{x}{b}}{\log_{x}{a}}$? Watch this video to find out what it is and how to use it.

$$ \frac{\log_{11}{5}}{\log_{11}{15}}=\log_{15}{5} $$

So, the answer is D.