Question

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

Answer 1

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(x), ln(x)` do not exist for `x<0.`

For `ln(x-2):`

`x-2=0`

`x=2`

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

As for horizontal asymptotes, logarithmic functions don't generally have any (at least in the forms `log_a(x), ln(x).`)