# How do you find the x intercept for f(x)=2log4(x)?

Dec 17, 2015

Solve for $x$ in $f \left(x\right) = 0$ to find that the $x$ intercept occurs at
$x = 1$.

#### Explanation:

An $x$-intercept occurs where $f \left(x\right) = 0$, and so to find any $x$-intercepts, we simply solve for $x$ in that equation.

We will be proceeding under the assumption that the question is regarding the base-$4$ log of $x$ (as opposed to the base $10$ or base $e$ log of $4 x$).

Using the property that ${a}^{{\log}_{a} \left(x\right)} = x$ we get

$2 {\log}_{4} \left(x\right) = 0$

$\implies {\log}_{4} \left(x\right) = 0$

$\implies {4}^{{\log}_{4} \left(x\right)} = {4}^{0}$

$\implies x = 1$