# How do you solve 2/3e^(4x)+1/3=4?

Aug 7, 2016

Let's start by isolating the ${e}^{4 x}$.

$\frac{2}{3} {e}^{4 x} = 4 - \frac{1}{3}$

$\frac{2}{3} {e}^{4 x} = \frac{11}{3}$

${e}^{4 x} = \frac{\frac{11}{3}}{\frac{2}{3}}$

${e}^{4 x} = \frac{11}{2}$

$\ln \left({e}^{4 x}\right) = \ln \left(\frac{11}{2}\right)$

$4 x \left(\ln \left(e\right)\right) = \ln \left(\frac{11}{2}\right)$

$4 x = \ln \left(\frac{11}{2}\right)$

$x = \frac{1}{4} \ln \left(\frac{11}{2}\right)$

Hopefully this helps!