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

1 Answer
Feb 11, 2018

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]}