Solving this exponential equation

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Homework Statement


Solve the equation e^x+10e^-x=7


Homework Equations


Logarithm rules and the natural logarithm



The Attempt at a Solution


Not really a calculus question but one I'm lost on nevertheless. I don't know how to go about solving this question at all. My first attempt was to factor out the e^x, but this got me nowhere. I know that this question has two answers (ln2 and ln5), but I cannot seem to figure out how to solve for these answers. Any help would be greatly appreciated, thanks in advance.
 
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Multiply both sides by e^x, which will give you an equation that is quadratic in form.
 

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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