Solving for x in equation (e^2x)-(3e^x)+2=0

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Homework Statement


Solve for x.
e2x-3ex+2=0


The Attempt at a Solution


e2x-3ex+2=0
-e2x+3ex=2
ex(3-ex)=2
lnex(3-ex)=ln2
x(3-ex)=ln2

..not very sure where to go here. Any direction would be appreciated! Thanks
 
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I wouldn't do what you wrote above. Start with this: let w = ex. Then rewrite the equation in terms of w. Does the equation look familiar now?
 

Thread 'Prove that the integral is equal to ##\pi^2/8##'

Prove $$\int\limits_0^{\sqrt2/4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx = \frac{\pi^2}{8}.$$ Let $$I = \int\limits_0^{\sqrt 2 / 4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx. \tag{1}$$ The representation integral of ##\arcsin## is $$\arcsin u = \int\limits_{0}^{1} \frac{\mathrm dt}{\sqrt{1-t^2}}, \qquad 0 \leqslant u \leqslant 1.$$ Plugging identity above into ##(1)## with ##u...
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