Question

Which of the following is the inverse of y=12^x

Answer 1

$y = 12^x$


$x = 12^y$

$12^y = x$

$\log 12^y = \log x$

$y \log 12 = \log x$

$y = \dfrac{\log x}{\log 12}$

Answer 2

$y=12^x\ \ \ |log_{12}\\\\\log_{12}y=\log_{12}12^x\\\\\log_{12}y=x\log_{12}12\\\\x=\log_{12}y$


$y=12^x\to y^{-1}=\log_{12}x;\ x\in\mathbb{R^+}\to\ y^{-1}=\dfrac{\log x}{\log12};\ x\in\mathbb{R^+}\to y^{-1}=\dfrac{\ln x}{\ln 12}$

$Used:\\\\\log_aa=1\\\\\log_ab^n=n\log_ab\\\\\log_ab=\dfrac{\log_cb}{\log_ca}$