$\displaystyle log{\sqrt{3}} $ 9
does it look like $\displaystyle \log_{\sqrt{3}}9$? if so, it is the base.
remember what a logarithm is, logarithms are powers.
Definition: the logarithm of a number to a given base is the power to which the base must be raised to give the number.
that is, if $\displaystyle \log_a b = c$ then $\displaystyle a^c = b$
example, $\displaystyle \log_28 = 3$ since we have to raise the base 2 to the power 3 to get 8
now, $\displaystyle \log_{\sqrt{3}}9$ is the power we have to raise $\displaystyle \sqrt{3}$ to to get 9. so what number is that?
what?! are you confused about something? where did 2 come from?
first of all, $\displaystyle 2^{\sqrt{3}}$ is not 9
second of all, there are no 2's here
third of all, we want to know what power we have to raise the base to, that is we want to solve $\displaystyle \sqrt{3}^x = 9$ for $\displaystyle x$