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Thread: Express (1/2) Log x - 2 Log x =y as a single Log

  1. #1

    Express (1/2) Log x - 2 Log x =y as a single Log

    (1/2) Log x - 2 Log x =y

    How do I simplify this to a single Log?

    I got Log .25 = y but I don't think it is correct. Can someone help me please. Thank you.

  2. #2
    Elite Member
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    [tex]\L y = \log \left( {\frac{{\sqrt x }}{{x^2 }}} \right)[/tex]
    “A professor is someone who talks in someone else’s sleep”
    W.H. Auden

  3. #3
    Elite Member
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    Re: Express (1/2) Log x - 2 Log x =y as a single Log

    Hello, pianoplaya16!

    Simplify to a single log: [tex]\:\frac{1}{2}\cdot\log(x)\,-\,2\cdot\log(x)[/tex]

    You're expected to know the properties of logs.

    [tex]\frac{1}{2}\cdot\log(x)\,-\,2\cdot\log(x)\;=\;\log\left(x^{\frac{1}{2}}\righ t)\,-\,\log\left(x^2\right) \;=\;\log\left(\frac{x^{\frac{1}{2}}}{x^2}\right)[/tex]

    . . [tex]=\:\log\left(x^{-\frac{3}{2}}\right)\;=\;-\frac{3}{2}\cdot\log(x)[/tex]

    I'm the other of the two guys who "do" homework.

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