Question

The values of x satisfying log₃ $(x^2+4x+12)=2$ are
(a) 2, −4
(b) 1, −3
(c) −1, 3
(d) −1, −3

Answer 1

(d) −1, −3

The given equation is ${\log }_3(x^2+4x+12)=2$.

$$\begin{gathered} \Rightarrow x^2+4x+12=3^2=9 \\ \Rightarrow x^2+4x+3=0 \\ \Rightarrow \left(x+1\right)\left(x+3\right)=0 \\ \Rightarrow x=-1,-3 \end{gathered}$$