Ramanujan's nested radical is great! (3)

Algebra Level 3

\[\large \displaystyle \prod_{k=2}^{2017}\sqrt[k]{2016\sqrt[k]{2016\sqrt[k]{2016\sqrt[k]{2016\sqrt[k]{\cdots}}}}}=\exp_{2016} \left( \sum_{n=1}^x \dfrac1n\right) \]

Find the value of \(x\) satisfying the equation above.

Notation: \( \exp_A (B) \) denotes the exponential function \(A^B\).

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