Find $x$ such that $\log_x 81=\log_2 16$.
One way to do that is to use the property of logarithms that says $\log_b a=c$ if and only if $b^c=a$. So I can rewrite the equation as $x^{\log_2 16}=81$. I notice that $16$ is a power of $2$, so I can rewrite $\log_2 16$ as $4$. This means the equation becomes $x^4=81$. To isolate $x$, I need to take the fourth root of both sides. The fourth root of $81$ is $3$, because $3^4=81$. So $x=3$. 