How do you find the inverse of $f(x)=log(x+7)$ ?

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Answer 1 · 2018-05-09T13:53:05

Since $ln$ or $log_e$ isn't used, I'll assume you are using $log_10$ but will provide a $ln$ solution too.

For $log_10(x+7)$ :
$y=log(x+7)$
$10^y=x+7$
$10^y-7=x$
$f^-1(x)=10^x-7$

For $ln(x+7)$ :
$y=ln(x+7)$
$e^y=x+7$
$e^y-7=x$
$f^-1(x)=e^x-7$

How do you find the inverse of f(x)=log(x+7)f(x)=log(x+7)?