Posted by **Moi** on Wednesday, December 8, 2010 at 8:42pm.

Hello, i was wondering if e^(2t) is equivalent to e^(t^2). I cant seem to find if this is true or not.

Thanks

- Logarithm law question -
**MathMate**, Wednesday, December 8, 2010 at 9:20pm
e^(2t) is equal to e^(t^2) *if and only if* t=2 or t=0, simply because 2t=t² for these two values of t.

Since in general, 2t≠t², e^(2t) is *not* equivalent to e^(t^2).

For example, t=4,

e^{2t}=e^{8}=2980.96

e^{t²}=e^{16}=8886110.52

The confusion arises probably because

e^{2t}=(e^{t})²

while

e^{t²}=(e^t)^t

Hope that clears it up.

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