Ramanujan's nested radical is great! (2)

Algebra Level 5

\[\large \frac{2016\sqrt{2016\sqrt[3]{2016\sqrt[4]{2016\sqrt[5]{2016\cdots}}}}}{\sqrt{2016\sqrt{2016\sqrt{2016\sqrt{2016\sqrt{2016\cdots}}}}}}=2016^{e+x}\]

Find \(x\) which satisfies the above equation.

Hint: Consider the infinite sum series of \(e\)

Clarification: \(e \approx 2.71828\) denotes the Euler's number.

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