# How do you solve the equation 0.16^(4+3x)=0.3^(8-x)?

Jan 29, 2017

$x = 0.29$

#### Explanation:

${0.16}^{4 + 3 x} = {0.3}^{8 - x}$

Take the log of both sides

$\log {0.16}^{4 + 3 x} = \log {0.3}^{8 - x}$

$\log {a}^{b} = b \log a$

$\left(4 + 3 x\right) \log 0.16 = \left(8 - x\right) \log 0.3$

$4 + 3 x = \log \frac{0.3}{\log} 0.16 \left(8 - x\right)$

Note: from this point on, it is better to use the exact value of $\log \frac{0.3}{\log} 0.16$, but for the sake of simplicity, a rounded value was used.

$4 + 3 x = 5.33 - 0.66 x$

$4.66 x = 1.33$

$x = \frac{1.33}{4.66} = 0.29$