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3 July, 01:53

If x=log3/5, y=log5/7, z=log root7/3, find the value of x+y+z

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  1. 3 July, 03:40
    0
    Given:

    x=log (3/5)

    y=log (5/7)

    z=log (sqrt (7/3)

    Find x+y+z

    Steps:

    Using the law of logarithms, log A + log B = log (AB), we get

    x+y+z

    =log (3/5) + log (5/7) + log (sqrt (7/3)

    =log (3/5*5/7*sqrt (7/3))

    =log (3/7*sqrt (7/3)

    =log ((sqrt (3/7) * sqrt (3/7) * sqrt (7/3))

    =log ((sqrt (3/7) * sqrt (3/7*7/3))

    =log (sqrt (3/7) * 1)

    =log (sqrt (3/7))

    Now apply another law of logarithms, log (sqrt (A)) = (1/2) log (A)

    = (1/2) log (3/7)

    which is the final answer.
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