A logarithmic function of the form f(x)= log_b x+c has an x-intercept at x= 1 and a vertical asymptote at y= 0. Also, f(x) intersects with the line y= 1 when x= 8. What is f(x)?

Question

Is it log_8 x+1?

Answer 1

I assume you are saying:
f(x) = log_b x + c
and (1,0) , (8,1) are on it.
using the first point:
0 = log_b 1 + c
0 = 0 + c , log 1 to any base = 0
c = 0
so y = log_b x
using the 2nd point
1 = log_b 8
b^1 = 8
b = 8
so f(x) = log₈ x

Your "a vertical asymptote at y= 0" makes no sense
that is like saying: there is a vertical asymptote at the x-axis.

However my equation has a vertical asymptote when x = 0

Answer 2

It was in the question, I don't know.

Thank you for your help!