# How do you find the inverse of f(x) = 3log(x-1)?

##### 1 Answer
Jul 19, 2015

I found: $f \left(x\right) = 1 + {10}^{\frac{x}{3}}$

#### Explanation:

I am not sure it is the "formal" way to do it but I do it like this:
I try to "extract" $x$:
$\log \left(x - 1\right) = \frac{f \left(x\right)}{3}$
assuming base $10$ for the log, I can write:
$x - 1 = {10}^{f \frac{x}{3}}$
$x = 1 + {10}^{f \frac{x}{3}}$
now I switch $x$ and $f \left(x\right)$ to get:
$f \left(x\right) = 1 + {10}^{\frac{x}{3}}$
Graphically:
$f \left(x\right) = 3 \log \left(x - 1\right)$
graph{3log(x-1) [-10, 10, -5, 5]}
and:
$f \left(x\right) = 1 + {10}^{\frac{x}{3}}$
graph{1+10^(x/3) [-10, 10, -5, 5]}