### Instruction: Evaluate $\log_3\frac{1}{\sqrt3}$.### Response: So what do we know about the log function?
That the log function with base $b$ is defined as $log_b(x)=y$ if $b^y=x$.
Right. So let's try to rewrite $\frac{1}{\sqrt3}$ as a power of 3.
Well, we know that $\sqrt3=3^{\frac{1}{2}}$, so that means that $\frac{1}{\sqrt3}=3^{\frac{-1}{2}}$.
Exactly. So now we can evaluate the log.
$\log_3\frac{1}{\sqrt3}=\log_3 3^{\frac{-1}{2}}=\frac{-1}{2}$