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Math Help - Simple Logs/Exp. Problem

  1. #1
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    Simple Logs/Exp. Problem

    Solve $3^{2x} - 3^{x+2} + 8 = 0$ for $x$.

    I tried:

    ${\log_{e} 3^{2x}} - {\log_{e} 3^{x+2}} + {\log_{e} 8} = 0$

    $\displaystyle{\frac{\log_{e} 3^{2x}}{\log_{e} 3^{x+2}}} + {\log_{e} 8} = 0$

    ${\log_{e} 3^{x - 2}} + {\log_{e} 8} = 0$

    $x = -\displaystyle{\frac{\log_{e} 8}{\log_{e} 3}} + 2$
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  2. #2
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    Re: Simple Logs/Exp. Problem

    This isn't correct.

    Try letting $u=3^x$ and see what you come up with.
    Last edited by romsek; March 21st 2014 at 04:40 PM.
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  3. #3
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    Re: Simple Logs/Exp. Problem

    Just checked again; doesn't work.

    From the book:

    $x = 0$ or $\displaystyle{\frac{\log_{e} 8}{\log_{e} 3}}$

    Thanks for the quick reply.
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  4. #4
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    Re: Simple Logs/Exp. Problem

    see my edited post.
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  5. #5
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    Re: Simple Logs/Exp. Problem

    Ahhh, one of those. Thank you.
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