Answer
$x \gt -\frac{3}{2}$.
Work Step by Step
The definition of the logarithmic function says that $y=\log_a{x}$ if and only if $a^y=x$. Also, $a\gt0,a\ne1$ and $x\gt0$.
By the definition of the logarithmic function we can only take the logarithm of a positive number, hence in the expression $\log_a {A}$ or $\ln {A}$, $A$ must be positive.
Hence $2x+3\gt 0\\2x\gt -3\\x \gt -\frac{3}{2}$.
