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Math Help - calculus review sheet - logs

  1. #1
    apm
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    calculus review sheet - logs

    i can't use a calculator
    solve for x:

    log3x^2=2log34 - 4log35

    i know that properties of logarithms but i'm not sure how i should use them to solve for x


    also how do you subtract logs of different bases
    simplify:
    2log49 - log23


    i appreciate any help
    Last edited by apm; August 15th 2008 at 07:57 PM. Reason: forgot something important
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  2. #2
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    Quote Originally Posted by apm View Post
    solve for x:

    log3x^2=2log34 - 4log35

    i know that properties of logarithms but i'm not sure how i should use them to solve for x


    also how do you subtract logs of different bases
    simplify:
    2log49 - log23


    i appreciate any help
    You can't subtract logs of different bases, as they're unlike terms. It's like asking what x-y is...

    But to answer your first question, to solve for x in this case you have to get both sides to be of the form \log_3 something...

    \log_3x^2=2\log_34-4\log_35
    \log_3x^2=\log_34^2-\log_35^4
    \log_3x^2=\log_3(\frac{4^2}{5^4})
    \log_3x^2=\log_3(\frac{4^2}{25^2})
    x^2=\frac{4^2}{25^2}
    x=\pm\frac{4}{25}
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  3. #3
    apm
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    thank you!
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