Math-Logarithmic function

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Find the equation of a logarithmic function whose graph has x-intercept 8, a vertical asymptote at x=0, and which passes through the point (1/2,4)

  • Math-Logarithmic function -

    Since I see numbers 1/2 , 4, and 8 I will use
    log2 as my logarithm

    Since the y-axis is an asymptote, there cannot be a horizontal shift of the standard log function, but there could be a vertical shift as well as a compression.

    let the function by
    y = alog2x + k
    point (8,0) is on it, so
    0 = alog28 + k
    0 = a(3) + k , (#1)

    point (1/2,4 lies on it, so
    4 = alog2(1/2) + k
    4 = a(-1) + k , (#2)

    subtract #1 from #2
    4 = -4a
    a = -1
    then 0 = -3+k
    k = 3

    so one possible log function would be

    y = - log2x + 3

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