What is the inverse of f(x) = 3log(x-1)?

May 20, 2018

$y = {\log}^{- 1} \left(\frac{x}{3}\right) + 1$

Explanation:

Set $y = 3 \log \left(x - 1\right)$

Divide both sides by 3

$\frac{y}{3} = \log \left(x - 1\right)$

${\log}^{- 1} \left(\frac{y}{3}\right) = x - 1$
$x = {\log}^{- 1} \left(\frac{y}{3}\right) + 1$
Wherever there was an $x$ write $y$ and wherever there was a $y$ write $x$ giving:
$y = {\log}^{- 1} \left(\frac{x}{3}\right) + 1$