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

Aug 3, 2018

The solution is $x = - 1.165$

#### Explanation:

Solve by taking the logs on both sides of the equation

${3}^{x + 4} = {2}^{1 - 3 x}$

$\ln \left({3}^{x + 4}\right) = \ln \left({2}^{1 - 3 x}\right)$

$\left(x + 4\right) \ln 3 = \left(1 - 3 x\right) \ln 2$

$x \ln 3 + 4 \ln 3 = \ln 2 - 3 x \ln 2$

$x \ln 3 + 3 x \ln 2 = \ln 2 - 4 \ln 3$

$x \left(\ln 3 + 3 \ln 2\right) = \ln 2 - 4 \ln 3$

$x = \frac{\ln 2 - 4 \ln 3}{\ln 3 + 3 \ln 2}$

$x = - \frac{3.701}{3.178} = - 1.165$