Logarithm law question
posted by Moi on .
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

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.