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Self Power to Googol (Posted on 2023-03-27)

Find x such that

x^x = 10¹⁰⁰

See The Solution Submitted by Charlie

Rating: 5.0000 (1 votes)

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Puzzle Solution

| Comment 3 of 4 |

We will implement Lambert's W-function, which is the inverse of f(x)= x*e^x

Let x=e^t

Then take the natural logarithm of both the sides to obtain

100*ln10 = t*e^t

=> t = W(100*ln10)

=> x = e^(W(100*ln10))

We get x= 56.961248432... using Wolfram Alpha.

Posted by K Sengupta on 2023-03-27 22:18:06

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