Chapter 12 - Exponential Functions and Logarithmic Functions - 12.6 Solving Exponential Equations and Logarithmic Equations - 12.6 Exercise Set - Page 826: 89

$x\in\{-1,-3\}$

On the LHS, apply $a^{m}\cdot a^{n}=a^{m+n}.$ On the RHS, recognize 27 as $3^{3},\displaystyle \quad\frac{1}{27}=3^{-3}$ $ 3^{x^{2}+4x}=3^{-3}\qquad$ ... apply the exponential equality principle $x^{2}+4x=-3$ $x^{2}+4x+3=0$ $(x+1)(x+3)=0$ $x=-1, x=-3$