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

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Answer 1 · 2018-05-20T16:41:32

$y=log^(-1)(x/3)+1$

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

Divide both sides by 3

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

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

$log^(-1)(y/3)=x-1$

$x=log^(-1)(y/3)+1$

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

$y=log^(-1)(x/3)+1$

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