Inverse of $$$y = 6^{x}$$$

To find the inverse function, swap $$$x$$$ and $$$y$$$, and solve the resulting equation for $$$y$$$.

This means that the inverse is the reflection of the function over the line $$$y = x$$$.

If the initial function is not one-to-one, then there will be more than one inverse.

So, swap the variables: $$$y = 6^{x}$$$ becomes $$$x = 6^{y}$$$.

Now, solve the equation $$$x = 6^{y}$$$ for $$$y$$$.

$$$y = \frac{\ln\left(x\right)}{\ln\left(6\right)}$$$

$$$y = \frac{\ln\left(x\right)}{\ln\left(6\right)}$$$A

Graph: see the graphing calculator.