^{x}=10

^{100}

Date: Fri, 25 Jul 1997 01:47:22 -0500

From: David Radcliffe

The equation x^{x}=10^{100} may be rewritten as
exp(ln(x))*ln(x) = 100*ln(10).

Lambert's W function is a function which satisfies the equation exp(W(x))*W(x) = x. That is, W is the inverse of f(x)=exp(x)*x. This function is mentioned in the FAQ for sci.math

Using this function, we get ln(x)=W(100*ln(10)), thus

x=exp(W(100*ln(10))).

David Radcliffe