graph the following logarithmic function: f(x)=log5 (x-1)-4

Question

critical point and domain

Answer 1

f(x) = ln(x-1)/ln5 - 4, using the change of base formula

f'(x) = 1/[(x-1)ln5)]

So, the critical point is at x = 1, and the domain is x > 1 since x-1>0.

You have a vertical asymptote at x = 1, no y-intercept, and the x-intercept is at x = 1+5^4. Can you sketch it now?

 

Another way to sketch it is to find its inverse y = 1+5^(x+4), and then reflect it about y = x to get f(x).