1. The problem is to explain how to use the inverse function to graph $f(x)=\log_6 x$. 2. Recall that the logarithm function $f(x) = \log_6 x$ is the inverse of the exponential function $g(x) = 6^x$. 3. To graph $f(x)=\log_6 x$, first graph the exponential function $y=6^x$. 4. The graph of $f(x)=\log_6 x$ is the reflection of the graph of $y=6^x$ across the line $y=x$. 5. Plotting points: For example, since $6^1=6$, the point $(1,6)$ is on $y=6^x$. 6. Reflecting across $y=x$ swaps coordinates, so $(1,6)$ on $y=6^x$ corresponds to $(6,1)$ on $y=\log_6 x$. 7. By reflecting multiple points from the exponential graph, you can accurately plot the logarithmic graph. 8. Key features are that the graph of $f(x)=\log_6 x$ passes through $(1,0)$ (since $\log_6 1=0$) and has a vertical asymptote at $x=0$. 9. Thus, using the inverse function and reflecting the exponential graph across $y=x$ gives the graph of the logarithm. Final answer: To graph $f(x)=\log_6 x$, graph $y=6^x$ first, then reflect that graph over the line $y=x$.