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Math Help - expand logrithmic expression

  1. #1
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    expand logrithmic expression

    How do I expand this:
    log_4\frac{2\sqrt[3]{x-5}}y^7

    Am I on the right path?:
    log_4(2(x-5))^{\frac{1}{3}}-y^7
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  2. #2
    Moo
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    Hello,

    A little typo :

    <br />
log_4\frac{2\sqrt[3]{x-5}}{y^7}<br />


    log_4(2(x-5))^{\frac{1}{3}}-y^7
    Not really, you forgot something important and you did a mistake in the brackets.

    It's actually \log_4(2(x-5)^{\frac{1}{3}})-\log_4(y^7)

    But the idea was good
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  3. #3
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    From there, what should my next step be?
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  4. #4
    Moo
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    Use the properties of logarithm :

    \log(xy)=\log(x)+\log(y)

    \log(a^b)=b\log(a)


    Do you need more indication ?
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  5. #5
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    log_4(2)+{\frac{1}{3}}log_4(x-5)-7log_4(y)?

    Are there any more steps? I think that is all I can expand it to.
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  6. #6
    Moo
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    I think this is perfect ^^

    One more thing :

    2=4^{1/2}

    Since \log_4(4)=1, do you think you can go further ?
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