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