Question

If ${\log }_3(2x+6)$ is defined, then the complete set of values of $x$ is

• A. $(-3,\infty )$
• B. $(6,\infty )$
• C. $(3,\infty )$
• D. $(-6,\infty )$

Answer 1

The correct option is A $(-3,\infty )$

${\log }_3(2x+6)$
Base $3>0$ and $3\ne 1$
$2x+6>0$
$\Rightarrow x>-3$
$\Rightarrow x\in (-3,\infty )$