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Math Help - Exponential Equations

  1. #1
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    Exponential Equations

    Solve each equation below. Express irrational solutions in exact form and as a decimal rounded to 3 decimal places.

    (1) (cuberoot{2})^(2 - x) = 2^(x^2)

    (2) e^(x + 3) = pi^(x)
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  2. #2
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    (\sqrt[3]{2})^{2-x} = 2^{x^2}

    (\sqrt[3]{2})^{2-x} = [(\sqrt[3]{2})^3]^{x^2}

    (\sqrt[3]{2})^{2-x} = (\sqrt[3]{2})^{3x^2}

    so ... what can you say about 2-x and 3x^2 ?


    e^{x+3} = \pi^x

    \ln(e^{x+3}) = \ln(\pi^x)

    x+3 = x\ln{\pi}

    3 = x\ln{\pi} - x

    3 = x(\ln{\pi} - 1)

    \frac{3}{\ln{\pi} - 1} = x
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  3. #3
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    Much better....

    This is much better than the other reply.
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