# What are the asymptotes for ln(x-2)?

Oct 10, 2015

Use the fact that it is a translation of $\ln x$

#### Explanation:

The graph of $y = \ln \left(x - 2\right)$ is the graph of $y = \ln x$ translated $2$ to the right.

$y = \ln x$ has vertical asymptote $x = 0$ (the $y$-axis).

When we translate the graph, we also translate any asymptotes,

so the new graph has asymptote $x = 2$.

Note We can also think of the fact that we'll get an asymptote when we try to find $\ln 0$, which happens for the new graph at $x = 2$.

Thirdly
For translations of $\ln x$, the asymptote occors at the bounded end of the domain.
The domain of $\ln \left(x - 2\right)$ is $\left(2 , \infty\right)$ so the asymptote is at $2$.
The asymptote is the vertical line $x = 2$.