[nwhsphcc] self exponentiation yielding googol

x^x = 10^100

solution x = 56.96124843

raising a number to its own power; self-power.  previously, Lambert W.

Mathematica:

u=100*Log[10]

N[u/ProductLog[u], 10]

Pari/GP:

solve(x=56, 57, x^x - 1e100)

(10^100 - epsilon) is the largest number representable on typical scientific calculators.  the solution joins factorial 69! ~= 1.7e+98 as the largest permitted inputs to scientific calculator functions that produce huge outputs from small imputs.