# How do you find the vertical, horizontal and slant asymptotes of: h(x) = log(x^2-4)/log(x/3)?

Nov 30, 2016

$x > 2$. x = 2 ($\uparrow$) and x = 3 are the vertical asymptotes, y = 2 ($\rightarrow$) is the horizontal asymptote. The x-intercept is $\sqrt{5}$.

#### Explanation:

h(x) is a bijective function for $x \in \left(2 , \infty\right)$.

$x > 2$. to make h real.

As $x \to {2}_{=} , y \to - \infty$.

As $x \to \infty , y \to 2$ ( from below ).

As $x \to 3 , y \to \pm \infty$

x = 2 ($\uparrow$) is the vertical asymptote, y = 2 ($\rightarrow$) is the

horizontal asymptote. The x-intercept is $\sqrt{5}$.

$y \in \left(- \infty , \infty\right)$.

The left portion of the graph is for $x \in \left(2 , 3\right]$

graph{y-log(x^2-4)/log(x/3)=0 [-41.92, 41.93, -20.94, 21]}