The given function is:
[tex]y=8^x-13[/tex]Make x the subject of the formula:
[tex]\begin{gathered} 8^x\text{ = y + 13} \\ \text{Take the natural logarithm of both sides} \\ \ln 8^x\text{ = ln (y + 13)} \\ x\ln \text{ 8 = }\ln (y+13) \\ x\text{ = }\frac{\ln (y+13)}{\ln 8} \end{gathered}[/tex][tex]\begin{gathered} \text{Let x be replaced by f}^{-1}(x)\text{ and y be replaced by x} \\ f^{-1}(x)\text{ = }\frac{\ln (x+13)}{\ln 8} \end{gathered}[/tex]