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5 May, 03:48

Simplify: log81/8 + 2log2/3 - 3log 3/2 + log 3/4

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  1. 5 May, 04:53
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    0.

    Step-by-step explanation:

    Using the laws of logarithms:

    log81/8 + 2log2/3 - 3log 3/2 + log 3/4

    = log 81/8 + log (2/3) ^2 - log (3/2) ^3 + log 3/4

    = log 81/8 + log 4/9 - log 27/8 + log 3/4

    = log 81/8 + log 4/9 - (log 27/8 - log 3/4)

    = log (81/8 * 4/9) - log (27/8 * 4/3)

    = log 9/2 - log 9/2

    = 0.
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