# Fun with natural log

• September 12th 2010, 05:31 PM
dn13
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!
• September 12th 2010, 05:55 PM
emakarov
You don't need logarithms for this. One has: $y = e^{3t} = (e^t)^3 = x^3$.
• September 13th 2010, 10:05 AM
ebaines
If you really want to use logs, you could do it like this:

$
ln(x) = t
$

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

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

$
y = x^3
$