Chapter 13 - Conic Sections - 13.2 Conic Sections: Ellipses - 13.2 Exercise Set - Page 862: 38

$x=3$

In order to find $x$ from the equation $$\log_{x}81=4$$ we will use rewrite the equation in exponential form: $$81=x^4$$ Calculate $x$: $$x=\pm\sqrt[4]{81}=\pm\sqrt[4]{3^4}=\pm 3$$ Because $x$ is the base of a logarithm in the given equation we must have $x>0,x\not=1$, so the only solution is $$x=3$$