# How do find the x-intercept of f(x)=2log4(x)?

Sep 29, 2015

$\left(\frac{1}{4} , 0\right)$

#### Explanation:

The x-intercept occurs where the graph intercepts the x-axis - in other words, where $f \left(x\right) = 0$. So, all we have to do is set $f \left(x\right)$ equal to $0$ and solve for $x$. Let's do it:

$0 = 2 \log 4 x$ (setting $f \left(x\right)$ equal to 0)
$0 = \log 4 x$ (dividing by $2$)
${10}^{0} = {10}^{\log 4 x}$ (10 to the power of both sides, to cancel out logarithm)
$1 = 4 x$ (simplifying; ${10}^{0} = 1$, ${10}^{\log 4 x} = 4 x$)
$x = \frac{1}{4}$ (dividing by $4$ to isolate $x$)

Thus, the x-intercept of $f \left(x\right) = 2 \log 4 x$ occurs at the point $\left(\frac{1}{4} , 0\right)$.