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Math Help - Logarithm simplification

  1. #1
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    Logarithm simplification

    I am having trouble solving this log.

    Simply:


    25^ log5(xy) + log ( xg * (root)y over (root) x)

    My simplification is:

    (xy)^2 + log (x^3/4 y^1/2 g /1)
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  2. #2
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    Do you mean

    A: 25^{\log_5(xy) + log_{10} \left(xg \sqrt{\dfrac{y}{x}\right)

    B: 25^{\log_5(xy)} + \log_{10}\left(xg \sqrt{\dfrac{y}{x}\right)

    C: Something entirely different
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  3. #3
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    Part B: but the x in the second log is also square rooted (in the denominator)
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  4. #4
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    so how would this be simplified?
    I can simplify the first part, but am having trouble with the second.
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  5. #5
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    ...

    so how would this be simplified?
    I can simplify the first part, but am having trouble with the second.
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  6. #6
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    So, you need to simplify:

    \displaystyle 25^{\log_5(xy)} + \log\left(xg \sqrt{\dfrac{y}{\sqrt{x}}\right)\ ?

    Your answer is correct.

    You may want to split up the logarithm to the sum of logarithms, depending upon what's meant by 'simplify'.
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  7. #7
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    Yes
    so would the second portion be:
    log(xg) + log(y^1/2) - log(x^1/4)
    log(x)+log(g)+log(y^1/2)-log(x^1/4)
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  8. #8
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    Quote Originally Posted by FallenStar117 View Post
    Yes
    so would the second portion be:
    log(xg) + log(y^1/2) - log(x^1/4)
    log(x)+log(g)+log(y^1/2)-log(x^1/4)
    You could also take the "1/2" and "1/4" out of the logarithms.
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