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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- Sep 12th 2010, 04:31 PMdn13Fun 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! - Sep 12th 2010, 04:55 PMemakarov
You don't need logarithms for this. One has: $\displaystyle y = e^{3t} = (e^t)^3 = x^3$.

- Sep 13th 2010, 09:05 AMebaines
If you really want to use logs, you could do it like this:

$\displaystyle

ln(x) = t

$

$\displaystyle

ln(y) = 3t = 3 ln(x)

$

$\displaystyle

e^{ln(y)} = e^{3 ln(x)} = e^{ln(x^3)}

$

$\displaystyle

y = x^3

$