# How do you simplify and solve (4^(2x)+3) + (4^(2x)+2) = 320?

Apr 4, 2015

${4}^{2 x} \cdot 2 = 315$

$\to {4}^{2 x} = \frac{315}{2}$

$\to \ln \left({4}^{2 x}\right) = \ln \left(\frac{315}{2}\right)$

$\to 2 x \ln \left(4\right) = \ln \left(157.5\right)$

$\to 2 x = \ln \frac{157.5}{\ln} \left(4\right)$

$\to 2 x \cong 3.64$

$\to x \cong 1.82$

Apr 4, 2015

Have a look:

At the end I used the change of base of logs where you have:
${\log}_{a} \left(c\right) = \ln \frac{c}{\ln} \left(a\right)$