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Math Help - Need help solving this logarithm

  1. #1
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    Need help solving this logarithm

    Write (equation) as the sum, difference, and/or constant multiple of logarithms.

    Equation is attached.
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  2. #2
    Moo
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    Hello,
    Quote Originally Posted by mwok View Post
    Write (equation) as the sum, difference, and/or constant multiple of logarithms.

    Equation is attached.
    For any base of the logarithm, you have :
    \log_a (xy)=\log_a(x)+\log_a(y)
    \log_a \left(\frac xy\right)=\log_a(x)-\log_a(y)
    \log_a (x^y)=y \log_a(x)

    ________________________________________________

    Note that \sqrt{z}=z^{1/2}
    \log_5 \left(\frac{x^3}{y z^{1/2}}\right)=\log_5(x^3)-\log_5(yz^{1/2})=\dots

    Can you finish it ?
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  3. #3
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    Thanks, attached is the solution I came up with (is it correct?).

    BTW, does the solution answer all parts of the question (as the sum, difference, and/or constant multiple of logarithms?)
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  4. #4
    Moo
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    Quote Originally Posted by mwok View Post
    Thanks, attached is the solution I came up with (is it correct?).

    BTW, does the solution answer all parts of the question (as the sum, difference, and/or constant multiple of logarithms?)
    Hey it's a z, not a 2 !

    And it's not a sum and difference of logarithms...

    Here is the thing :

    \log_5 \left(\frac{x^3}{y z^{1/2}}\right)=\log_5(x^3)-\log_5(yz^{1/2})
    =3 \log_5(x) \quad - \quad \left(\log_5(y)+\log_5(z^{1/2})\right)
    =3 \log_5(x)-\log_5(y)-\frac{\log_5(z)}{2}

    This is what you're asked to find. Do you understand the steps ? And what they mean by "sum, difference, and/or constant multiple of logarithms" ?
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  5. #5
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    Thanks! Ah I see the solution and understand the steps.


    But what do they mean by "sum, difference, and/or..."?

    Does it mean just show the equation as a sum/difference of logarithms? Like in this case, we've shown a difference of logarithms?
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