## Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (3rd Edition)

$x=\dfrac{-5+3 \sqrt{5}}{2} \approx 0.854$
Apply the logarithmic property : $\log_a M+\log_a N = \log_a (MN)$ and rearrange the given expression to obtain: $\log_3[(x+1)(x+4)]$ Since, $\log_m{n} = 1$ gives: $m^{(1)}=n$, then we have: $\log_3(x^2+5x+4)=2$ $x^2+5x+4=3^2$ or, $x^2+5x-5=0$ This is a quadratic equation; thus by using the quadratic formula $x=\dfrac{-b \pm \sqrt{b^2-4ac}}{2a}$, we get: $x=\dfrac{-5 \pm 3 \sqrt{5}}{2(1)}$ or, $x=\dfrac{-5 + 3 \sqrt{5}}{2}, \dfrac{-5 -3 \sqrt{5}}{2}$ Since, the domain of the variable is $x \gt 0$, we cannot accept the value of $x=\dfrac{-5 -3 \sqrt{5}}{2}$ Thus, our answer is: $x=\dfrac{-5+3 \sqrt{5}}{2} \approx 0.854$