Question

How do you graph `y=log_6(x-1)-5`?

Answer 1

graph{log(x-1)/log(6)-5 [-1.75, 18.25, -9.28, 0.72]}

Explanation:

The first step would be to know how the basic `log(x)` function looks:
graph{log(x) [-2, 18, -5.56, 4.44]}
Notice two certain coordinate pairs: `(1, 0)` and `(10, 1)`

As you may know `log(x) = log_10(x)`

If we were to graph `log_6(x)` we would be able to deduce the coordinate pairs `(1, 0)` and `(6, 1)`

Now to graph your requested function of `log_6(x-1) -5`

We simply apply a phase-shift of 1 unit to the right and 5 units down. We know this because of simple transformation concepts concerning functions.

So we get:
graph{log(x-1)/log(6)-5 [-1.75, 18.25, -9.28, 0.72]}