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Math Help - Fun with natural log

  1. #1
    Newbie
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    Fun with natural log

    how do I turn this:
    x = e^t and y = e^3t

    into: y = x^3?

    I tried this:

    lnx = t, lny = 3t

    lnx = lny/3

    3lnx^3 = lny

    e^x3 = e^y

    Thanks!
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  2. #2
    MHF Contributor
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    You don't need logarithms for this. One has: y = e^{3t} = (e^t)^3 = x^3.
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  3. #3
    MHF Contributor ebaines's Avatar
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    If you really want to use logs, you could do it like this:

    <br />
ln(x) = t <br />
     <br />
ln(y) = 3t = 3 ln(x)<br />
     <br />
e^{ln(y)} = e^{3 ln(x)} = e^{ln(x^3)}<br />
     <br />
y = x^3<br />
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