Chapter 12 - Exponential Functions and Logarithmic Functions - 12.6 Solving Exponential Equations and Logarithmic Equations - 12.6 Exercise Set - Page 826: 83

$x=-1$ , $x=-3$

Recognize 8 as a power of 2. $ 2^{x^{2}+4x}=\displaystyle \frac{1}{2^{3}}\qquad$ ... apply $a^{-n}=\displaystyle \frac{1}{a^{n}}$ $ 2^{x^{2}+4x}=2^{-3}\qquad$ ... apply the exponential equality principle $x^{2}+4x=-3$ $x^{2}+4x+3=0$ .. find factors of $c=3$ whose sum is $b=4$ ... we find $+1$ and $+3.$ $(x+1)(x+3)=0$ $x=-1$ , $x=-3$