# How do you find the vertical asymptote of a logarithmic function?

##### 1 Answer
Oct 28, 2015

The vertical asymptote is (are) at the zero(s) of the argument and at points where the argument increases without bound (goes to $\infty$).

#### Explanation:

$f \left(x\right) = {\log}_{b} \left(\text{argument}\right)$ has vertical aymptotes at $\text{argument} = 0$

Example $f \left(x\right) = \ln \left({x}^{2} - 3 x - 4\right) .$ has vertical asymptotes

$x = 4$ and $x = - 1$

graph{y=ln(x^2-3x-4) [-5.18, 8.87, -4.09, 2.934]}

Example $f \left(x\right) = \ln \left(\frac{1}{x}\right)$ has vertical asymptote

$x = 0$

graph{ln(1/x) [-5.18, 8.87, -4.09, 2.934]}

Example $f \left(x\right) = \ln \left(\frac{1}{x} ^ 2\right)$ alsohas vertical asymptote

$x = 0$

graph{ln(1/x^2) [-5.18, 8.87, -4.09, 2.934]}