Advanced Functions/ Precalculus Log

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If (x, y) is on the graph f(x) = log(base10)x, state the coordinates (in terms of x and y) that would be on the graph of f(x) = 2log(base10)(x - 4) + 3?

Can you please explain how to answer this question? Thanks!

  • Advanced Functions/ Precalculus Log -

    remember if the base of the log is 10, we don't have to write the base.

    so you have y= logx
    and y = 2log(x-4)+3

    intersection:
    2log(x-4) + 3 = logx
    log(x-4)^2 - logx = -3
    log ( (x-4)^2 /x ) = -3

    (x-4)^2 /x = 10^-3
    x^2 - 8x + 16 = (1/1000)x
    1000x^2 - 8001x + 16000=0
    using the formula
    x = (8001 ± 126.5)/2000
    = 4.06 or 3.94

    but in 2log(x-4) , x-4> 0 , so our 2nd answer is rejected

    x = appr 4.06

    if x = 4.06, then y = log 4.06 = appr .61

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