the natural log, ln, is the inverse of the exponential.
so you can take the natural log of both sides of the equation and you get...
ln(e^(x))=ln(.4634)
ln(e^(x))=x because ln and e are inverses
so we are left with x = ln(.4634)
x = -0.769165
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The power law of indices says: (x^a)^b = x^(ab) = x^(ba) = (x^b)^a → e^(2x) = (e^x)² but e^x = 2 → e^(2x) = (e^x)² = 2² = 4
-2y square exp power -2x-1
ex = x3 This has two solutions: x = 4.5364... and x = 1.85718... Plot the graph of each and you can see the intersections.
integral of e to the power -x is -e to the power -x
Because the derivative of e^x is e^x (the original function back again). This is the only function that has this behavior.