Answer
$ x=\pm 2$
Work Step by Step
$\log _{2}\sqrt {2x^{2}}=\dfrac {3}{2}\Rightarrow \sqrt {2x^{2}}=2^{\dfrac {3}{2}}\Rightarrow \left( 2x^{2}\right) ^{\dfrac {1}{2}}=8^{\dfrac {1}{2}}\Rightarrow 2x^{2}=8\Rightarrow$
$ x=\pm 2$
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