precalculus

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write the expression below as a single logarithm show work.

ln(x-7/x^2+12x+36)-ln(x^2-49/x+6)

  • precalculus -

    first
    x^2+12x+36 = (x+6)(x+6)
    so

    ln of

    (x-7)(x+6)
    =====================
    (x+6)(x+6)(x+7)(x-7)

    ln of

    1
    =====================
    (x+6)(x+1)

    = ln 1 - ln(x^2 +7x + 6)
    but ln 1 = 0
    so
    - ln (x^2 + 7 x + 6)

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