# How do you find the asymptotes for ln(x-2)?

Feb 28, 2018

Vertical asymptote at $x = 2.$

#### Explanation:

A logarithmic function has a vertical asymptote at $x = c$ where $c$ is the value of $x$ causes the argument inside the parentheses to become $0.$ This is because ${\log}_{a} \left(x\right) , \ln \left(x\right)$ do not exist for $x < 0.$

For $\ln \left(x - 2\right) :$

$x - 2 = 0$

$x = 2$

Is the vertical asymptote, as for values less than $x = 2 , \ln \left(x - 2\right)$ doesn't exist.

As for horizontal asymptotes, logarithmic functions don't generally have any (at least in the forms ${\log}_{a} \left(x\right) , \ln \left(x\right) .$)