Question

Rewrite as a quotient of two base- 5 logarithms. Write your answer in simplest form. log 9 =

Answer 1

$\log(9)=\log_{10}(9)=\dfrac{\log_{5}(9)}{\log_{5}(10)}$

In my opinion, that is the simplest form. However, your teacher may want you to remove powers and factors of 5. In that case, the result is ...

$=\dfrac{\log_{5}(3^{2})}{\log_{5}(5\cdot 2)}=\dfrac{2\log_{5}(3)}{1+\log_{5}(2)}$