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)?

Is it log_8 x+1?

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

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

    Thank you for your help!

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