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  1. #1
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    Logs

    Calculate the ratio x/y if 2log5(x-3y)=log5(2x)+log5(2y)
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  2. #2
    Super Member General's Avatar
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    Quote Originally Posted by Tiger View Post
    Calculate the ratio x/y if 2log5(x-3y)=log5(2x)+log5(2y)
    2\log_{5}(x-3y)=\log_{5}(2x)+\log_{5}(2y)
    \log_{5}(x-3y)^2=\log_{5}(4xy)
    (x-3y)^2=4xy
    Now, devide both sides by 4x to obtain a formula for y.
    and then deivde both sides by 4y to obtain a formula for x.
    Hence, You got a formula for x and a formula for y.
    Then you are able to find the ratio \frac{x}{y}.
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  3. #3
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by Tiger View Post
    Calculate the ratio x/y if 2log5(x-3y)=log5(2x)+log5(2y)
    First note that x,y > 0. Now,

    2 \log_5 (x - 3y) = \log_5 (2x) + \log_5 (2y)

    \Rightarrow \log_5 (x - 3y)^2 = \log_5 (4xy)

    \Rightarrow (x - 3y)^2 = 4xy

    \Rightarrow x^2 - 10xy + 9y^2 = 0

    \Rightarrow (x - 9y)(x - y) = 0

    So that x - 9y = 0 \implies \boxed{ \frac xy = 9}

    or

    x - y = 0 \implies \boxed{\frac xy = 1}
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  4. #4
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by General View Post
    2\log_{5}(x-3y)=\log_{5}(2x)+\log_{5}(2y)
    \log_{5}(x-3y)^2=\log_{5}(4xy)
    (x-3y)^2=4xy
    Now, devide both sides by 4x to obtain a formula for y.
    and then deivde both sides by 4y to obtain a formula for x.
    Hence, You got a formula for x and a formula for y.
    Then you are able to find the ratio \frac{x}{y}.
    This doesn't work. you would get x/y = x/y, which isn't helpful
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