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Math Help - Laws of Logarithms

  1. #1
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    Laws of Logarithms

    Evaluate:

    log_28^{27} - log_464^{\frac {1}{5}}


    My work:

    = log_2(2^{3})^{27} - log_4 \sqrt [5] {64}

    = log_2 2^{81} - \frac {1}{5} log_464

    =  81 log_22 - \frac {1}{5} log_44^{3}


    And now what do I do? I don't know how to put both in the same base
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  2. #2
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    next step:

    81*(log2/log2) - (3/5)*(log4/log4)

    You can do the rest.

    I think thats it, if your initial reasoning is correct.
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  3. #3
    Senior Member DivideBy0's Avatar
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    Melbourne, Australia
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    Quote Originally Posted by Macleef View Post
    Evaluate:

    log_28^{27} - log_464^{\frac {1}{5}}


    My work:

    = log_2(2^{3})^{27} - log_4 \sqrt [5] {64}

    = log_2 2^{81} - \frac {1}{5} log_464

    = 81 log_22 - \frac {1}{5} log_44^{3}


    And now what do I do? I don't know how to put both in the same base
    You've done very well so far. All that's needed now is to realise that \log_aa^b=b (convert back into exponential form to confirm this)

    So 81\log_22^1-\frac{1}{5}\log_44^3=81\times 1 - \frac{1}{5} \times 3=\frac{402}{5}
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