Answer
$\log _{a}\dfrac {25x^{6}}{\sqrt {\left( 2x+3\right) }}$
Work Step by Step
$2\log _{a}\left( 5x^{3}\right) -\dfrac {1}{2}\log _{a}\left( 2x+3\right) =\log _{a}\dfrac {\left( 5x^{3}\right) ^{2}}{\left( 2x+3\right) ^{1/2}}=\log _{a}\dfrac {25x^{6}}{\sqrt {\left( 2x+3\right) }}$
