Answer :
Replace the variable y with x and varaible with y.
[tex]x=2\log (y)-8[/tex]Simplify the equation for y.
[tex]\begin{gathered} x=2\log y-8 \\ x+8=2\log y \\ \log y=\frac{x+8}{2} \\ y=10^{\frac{x+8}{2}} \end{gathered}[/tex]So inverse of the function is,
[tex]y=10^{\frac{x+8}{2}}[/tex]