Question

The values of x satisfying log₃ \[( x^2 + 4x + 12) = 2\] are

Options

• 2, −4

• 1, −3

• −1, 3

• −1, −3

Answer 1

−1, −3 The given equation is \[\log_3 ( x^2 + 4x + 12) = 2\] .

\[\Rightarrow x^2 + 4x + 12 = 3^2 = 9\]

\[ \Rightarrow x^2 + 4x + 3 = 0\]

\[ \Rightarrow \left( x + 1 \right)\left( x + 3 \right) = 0\]

\[ \Rightarrow x = - 1, - 3\]