Name: Anonymous 2009-02-11 22:34
Hey /sci/,
In a problem I'm doing I've got e^(1/2 ln|x^2+1|). Somehow this becomes sqrt(x^2+1).
My guess is that when you have e^(ab) you get (e^b)^a, which in this case where a = 1/2 and b = ln|x^2+1|, you get e^ln|x^2+1| = (x^2+1)^1/2 = sqrt(x^2+1). I don't understand why this would happen though.
Can someone please explain why this happens, or at least tell me if I'm right in my guess that e^(ab) = (e^b)^a?
In a problem I'm doing I've got e^(1/2 ln|x^2+1|). Somehow this becomes sqrt(x^2+1).
My guess is that when you have e^(ab) you get (e^b)^a, which in this case where a = 1/2 and b = ln|x^2+1|, you get e^ln|x^2+1| = (x^2+1)^1/2 = sqrt(x^2+1). I don't understand why this would happen though.
Can someone please explain why this happens, or at least tell me if I'm right in my guess that e^(ab) = (e^b)^a?