How do you solve 22=44(1-e^(2x))?

Dec 19, 2016

Answer:

I got: $x = \frac{\ln \left(\frac{1}{2}\right)}{2} = - 0.34657$

Explanation:

Let us rearrange it as:
$1 - {e}^{2 x} = \frac{22}{44}$
$1 - {e}^{2 x} = \frac{1}{2}$
${e}^{2 x} = 1 - \frac{1}{2}$
${e}^{2 x} = \frac{1}{2}$
take the natural log of both sides:
$\ln \left({e}^{2 x}\right) = \ln \left(\frac{1}{2}\right)$
$2 x \ln \left(e\right) = \ln \left(\frac{1}{2}\right)$
but $\ln \left(e\right) = 1$
so:
$2 x = \ln \left(\frac{1}{2}\right)$
$x = \frac{\ln \left(\frac{1}{2}\right)}{2} = - 0.34657$