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Math Help - solving equations with logs

  1. #1
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    solving equations with logs

    Hi, I have a question with 2 parts regarding logs, i have done the first part and believe very close to the second part but cannot quite get there and was wondering if someone could please help me?

    a) show log4(3)=log2(root3)

    but i am stuck with this part:

    b) solve these simultaneous equations
    2log2(y)=log4(3)+log2(x) and 3^y=9^x

    any help with this would be great

    thanks for your time
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  2. #2
    Super Member Failure's Avatar
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    Quote Originally Posted by wahhdoe View Post
    Hi, I have a question with 2 parts regarding logs, i have done the first part and believe very close to the second part but cannot quite get there and was wondering if someone could please help me?

    a) show log4(3)=log2(root3)

    but i am stuck with this part:

    b) solve these simultaneous equations
    2log2(y)=log4(3)+log2(x) and 3^y=9^x

    any help with this would be great

    thanks for your time
    From the second equation, 3^y=9^x, you get 3^y=3^{2x}, and, therefore, y=2x. Now plug this into the first equation. - What do you get?
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  3. #3
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    yeah i got y=2x as well but then i get this:

    log2(4x^2)-log2(x)-log2(root3)=0

    and i still cannot solve this
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  4. #4
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    Quote Originally Posted by wahhdoe View Post
    yeah i got y=2x as well but then i get this:

    log2(4x^2)-log2(x)-log2(root3)=0

    and i still cannot solve this
    Work on the LHS with using \log_ab-\log_ac = \log_a\frac{b}{c}

    Then change the RHS into \log_21
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