Answer
$x=\dfrac {4}{3}$
Work Step by Step
$\left( \sqrt {2}\right) ^{x+4}=4^{x}\Rightarrow 2^{\dfrac {1}{2}\left( x+4\right) }=2^{2x}\Rightarrow \dfrac {1}{2}\left( x+4\right) =2x\Rightarrow \dfrac {3x}{2}=2\Rightarrow x=\dfrac {4}{3}$
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