I have a homework problem that I am struggling to understand. The problem is Find a formula for the inverse function $f^ {-1}$ of the function $f$. $f(x)=\log_{2x}3$
Here is my attempt at solving this problem. $y=\log_{2x}3$ $2x ^y=3$ $x^y=3/2$ $(x ^y)^{1/y}=\left(\frac{3}{2}\right)^{1/y}$ $x=\left(\frac{3}{2}\right)^{1/y}$
However, the answer in the book is $\frac{3^{1/y}}{2}$. I think I know my mistake but I am not sure why it is wrong. I believe that my mistake was when I divided $2$ from $2x^y$, are you not allowed to do that?