Question

What is the inverse of 2(3)^x
Please and thank you

Answer 1

as you already know, to get the inverse of any expression we start off by doing a quick switcheroo on the variables and then solving for "y", let's do so.

`y~~ = ~~2(3)^x\hspace{5em}\stackrel{\textit{quick switcheroo}}{x~~ = ~~2(3)^y} \\\\\\ \cfrac{x}{2}=3^y\implies \log\left( \cfrac{x}{2} \right)=\log(3^y) \implies \log\left( \cfrac{x}{2} \right)=y\log(3) \\\\\\ \cfrac{\log\left( (x)/(2) \right)}{\log(3)}=y\implies \log_3\left( (x)/(2) \right)=y=f^(-1)(x)`