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e2x=ex^2 basically means that x2=2x, in which case x2-2x=0, x = 0, 2.

I don't think that's what the question meant. It could mean: e2x=(ex)2 . Which comes from one of the rules of exponents. Basically, look at it this way:

Take the natural log of both sides: ln e2x= ln(ex)2

From rules of logs:

(2x) ln e = (2) ln ex

2x ln e = (2) (x) ln e

2x = (2)(x)

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12y ago
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Q: How does e raised to the power of 2x equal e raised to the power of x squared?
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