exponential equation (solve for x)

Question

We started review in my calculus class and I have mostly forgotten everything about exponential equations.

$$ e^{-x} * (3e^{2x}-(5/4))^{1/2} = e^x $$

Would x just equal 0, when -x+x=0 (two sides of the $e$ exponents).

Answer 1

Multiplying both sides by $e^x$ and squaring both sides gives you

$$3e^{2x}-\frac{5}{4} = e^{4x}.$$

Setting $y=e^{2x}$, you get a quadratic equation $y^2 - 3y + \frac{5}{4}=0$, and you should be able to solve for $y$ and then $x$ from there.