[tex]y=\log _8x[/tex]
To find the inverse of the logarithmic function, let's switch the places of x and y. It becomes:
[tex]x=\log _8y[/tex]
After that, let's convert the logarithmic function to its equivalent exponential function.
[tex]\begin{gathered} 8^x=y \\ 8^x=f^{-1}(x) \end{gathered}[/tex]
The inverse of the logarithmic function is 8^x.
Let's graph the two equations.
We labeled two points on each graph. As you can see, the points are at an equal distance from the line x = y, therefore, we got the correct inverse of the logarithmic function.
