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

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Answer 1 · 2018-05-20T16:41:32

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

Set $y = 3 log (x - 1)$ $y=3log(x-1)$

Divide both sides by 3

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

Using older terminology: tale the antilogarithm of both sides (log inverse).

${log}^{- 1} (\frac{y}{3}) = x - 1$ $log^(-1)(y/3)=x-1$

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

Wherever there was an $x$ $x$ write $y$ $y$ and wherever there was a $y$ $y$ write $x$ $x$ giving:

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

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