Question:
The values of $x$ satisfying $\log _{3}\left(x^{2}+4 x+12\right)=2$ are
(a) 2, −4
(b) 1, −3
(c) −1, 3
(d) −1, −3
Solution:
(d) −1, −3
The given equation is $\log _{3}\left(x^{2}+4 x+12\right)=2$.
$\Rightarrow x^{2}+4 x+12=3^{2}=9$
$\Rightarrow x^{2}+4 x+3=0$
$\Rightarrow(x+1)(x+3)=0$
$\Rightarrow x=-1,-3$
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