What is the value of s? [duplicate]

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This is something I came up with a day. I tried a procedure but later I found it was incorrect. So here it is:

$$2^s = 2s + 2 $$

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1 Answer

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As the commentators have written, the solution involves the Lambert W-function. Look it up.

The explicit solution according to Wolfy is$s = -\dfrac{W(-\log(2)/4) + \log(2)}{\log(2)} $.

The numeric values for the two branches of the W-function are$s≈-0.690093 $for the main branch and$s = 3$for the -1 branch.

Yep - $2^3 = 2\cdot 3 + 2$.

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