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Math Help - Rewriting Equation

  1. #1
    Member WhoCares357's Avatar
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    Rewriting Equation

    I have to express the following two equations as a power of e.

    a) \pi^x
    b) x^(2x), x > 0

    I don't necessarily need the answers. Rather an explanation or a link to an explanation would suffice.

    Thank you.

    Edit: The question was so simple that I overthought it. a) is just e^(-x*ln(pi))
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  2. #2
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    Hello, WhoCares357!

    Express the following functions as a power of e.

    a)\;\;y \:=\:\pi^x
    Take logs: . \ln(y) \:=\:\ln(\pi^x) \quad\Rightarrow\quad \ln(y) \:=\:x\ln(\pi)

    Exponentiate: . y \;=\;e^{x\ln(\pi)}




    b)\;\;y \:=\:x^{2x},\;\;x > 0
    Take logs: . \ln(y) \;=\;\ln(x^{2x}) \quad\Rightarrow\quad \ln(y) \;=\;2x\ln(x)

    Exponentiate: . y \;=\;e^{2x\ln(x)}

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