mathematics

expand: In((3x-5)1/2 )/7

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  1. I believe you meant to type
    In((3x-5)^1/2 )/7.

    See the difference. You forgot to raise (3x - 5) to the 1/2 power.

    Use the log rule for division:

    ln(a/b) = ln(a) - ln(b).

    ln((3x - 5)^1/2) - ln(7)

    Note: (3x - 5)^1/2 is sqrt{3x - 5} in disguise.

    Answer:

    ln(sqrt{3x - 5}) - ln(7)

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  2. Perhaps one step further ...

    ln((3x - 5)^1/2) - ln(7)
    = (1/2) ln(3x-5) - ln 7

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