Math - Logarithm

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Solve the following logarithm equation. Please show all of your work.
log (5 + x) – log(x – 2) = log 2

  • Math - Logarithm -

    log (5 + x) – log(x – 2) = log 2
    log [(5+x)/(x-2)] = log 2

    (5+x)/(x-2) = 2
    2x - 4 = 5+x
    x = 9

  • Math - Logarithm -

    Use law of logarithms,
    log(a)-log(b)=log(a/b)

    So
    log (5 + x) – log(x – 2) = log 2
    =log((5+x)/(x-2))=log2
    Take anti-log on both sides
    (5-x)/(x-2)=2
    (5-x)=2(x-2)
    Solve for x.

  • Math - Logarithm -

    (5+x)/(x-2)=2

    5+x=2*(x-2)

    5+x=2x-4

    5+4=2x-x

    9=x

    x=9

  • Math - Logarithm -

    −6ln(x) − 8ln(y) +
    1
    8
    ln(z)

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