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Evaluate log(6)√6 (actual question)

There's a problem in my book that says:

Convert each logarithm to a natural logarithm and evaluate log(5)√288
the answer in the back is 1.7593 but I can't find an example of those kinds.

  • Math -

    your book should show two of several important properties of logs
    1. loga a = 1
    2. loga b = log10 a/log10 b

    in log(5)√288 they used #2 rules
    = log(√288)/log 5
    = log(16.97056275)/log5
    = 1.22969244/.69897 1.759297

    for the first of your questions we don't even have to use that

    log6 √6
    = (1/2)log6 6
    = (1/2)(1)
    = 1/2

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