If $\displaystyle \left(\frac{3}{4}\right)^x=\frac{81}{256}$, what must $x$ be?
I recognize that both $\displaystyle \frac{3}{4}$ and $\displaystyle \frac{81}{256}$ are powers of $\displaystyle \frac{3}{4}$, so I can write them as $\displaystyle \left(\frac{3}{4}\right)^1$ and $\displaystyle \left(\frac{3}{4}\right)^4$ respectively. This means that the equation becomes $\displaystyle \left(\frac{3}{4}\right)^x=\left(\frac{3}{4}\right)^4$. Since the bases are the same, I can equate the exponents and get $x=4$. 