Question

How do you find the domain, x intercept and vertical asymptotes of `g(x)=log_6x`?

Answer 1

Domain: `x>0`, vertical asymptote: `x=0`, `x`-intercept: `(1,0)`.

Explanation:

You cannot take the log of a negative number and there is no power to which you can raise 6 and get 0, so the domain is `x>0`.

The vertical asymptote of a log function is at the end of its domain, so the vertical asymptote is `x=0`.

To find the `x`-intercept we set `log_6x=0`

Solve we have:
`log_6x=0\rightarrow 6^0=x\rightarrow x=1`, so the `x`-intercept is `(1,0)`.