$\log_{\sqrt{3}} 81 = ?$ (Example 6)

Let $\log_{\sqrt 3} 81 = x$, so $(\sqrt 3)^x = 81 = 3^4$. Since $(\sqrt 3)^x = 3^{x/2}$, we get $\dfrac{x}{2} = 4$, hence $x = 8$.