Ramanujan's nested radical is great! (2)

Algebra Level 5

20162016201620162016⋯54320162016201620162016⋯=2016e+x\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 xx which satisfies the above equation.

Hint: Consider the infinite sum series of ee

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

Tommy Li by Tommy Li
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