Question

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

Answer 1

Use the fact that it is a translation of `lnx`

Explanation:

The graph of `y=ln(x-2)` is the graph of `y=lnx` translated `2` to the right.

`y=lnx` 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 `ln0`, which happens for the new graph at `x=2`.

Thirdly
For translations of `lnx`, the asymptote occors at the bounded end of the domain.
The domain of `ln(x-2)` is `(2,oo)` so the asymptote is at `2`.
The asymptote is the vertical line `x=2`.