Question

How do i solve e^2x-5e^x+6=0

Answer 1

Substitute u=e^x to turn it into a quadratic equation. After you have the solution, substitute back the to the original terms and solve. Remember that an exponential is never negative....

Answer 2

So u=e^x, then\[0=e ^{2x} -5e^x+6=u^2-5u+6=(u-2)(u-3)\rightarrow u=e^x=2 or 3\]So the solutions for x are x=ln(2) or x=ln(3)