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Thread: Exponential equations?

  1. #1
    Member Kaloda's Avatar
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    Question Exponential equations?

    Solve for $\displaystyle x$ in the inequality $\displaystyle 5^x> 25^2^x$.
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by Kaloda View Post
    Solve for $\displaystyle x$ in the inequality $\displaystyle 5^x> 25^2^x$.
    Take logs:

    $\displaystyle x\ln(5)>2x \ln(25)=2x \ln(5^2)=4x \ln(5)$

    CB
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  3. #3
    MHF Contributor
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    An easier way

    $\displaystyle 5^x > 25^{2x}$

    $\displaystyle 5^x > (5^2)^{2x}$

    $\displaystyle 5^x > 5^{4x}$

    $\displaystyle x > 4x$

    $\displaystyle 0 > 3x$

    $\displaystyle 0 > x$.
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