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Math Help - which grows fastest?

  1. #1
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    which grows fastest?

    Which of the following functions grow faster then e^x as x approaches infinity?

    x^4
    ln(x)
    e^(-x)
    3^x
    .5*e^x
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  2. #2
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    3^x because it is e^(xln 3) while e^x is just e^(x*1) and ln 3 > 1.
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  3. #3
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    Quote Originally Posted by ThePerfectHacker View Post
    3^x because it is e^(xln 3) while e^x is just e^(x*1) and ln 3 > 1.
    Another reason as to why...

    3^x > e^x

    Same exponent, but the left side has a larger base hence a larger outcome, and to connect this to TPH's explanation..

    ln|3|x > x

    x \ne 0 <- this follows because at zero the functions are equal

    ln|3| > 1
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