Discrete Mathematics

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If f(x) = log2 (x - 2)3 and g(x) = log8 (x - 2), when is (f + g)(x) = 0?

  • Discrete Mathematics -

    working with logs base 2,
    since 8=2^3, g(x) = 1/3 log(x-2)

    (f+g)(x) = f(x)+g(x)
    = 3log(x-2) + 1/3 log(x-2)
    = 10/3 log(x-2)

    so, if (f+g)(x) = 0,
    log(x-2) = 0
    x-2 = 1
    x = 3

    check

    log_2(3-2)^3 = 0
    log_8(3-2) = 0

  • Discrete Mathematics -

    Thanks Steve! I am starting to write these down so that way I will understand them. It is easier for me to go off an example. I appreciate all your help.

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