\(x^lg(x)=100^x\)
\(X^lg(x)=100^x:x\) \(|Solve \ for \ x|\)
\(|Use \ logarithms \ of \ both \ sides \ of \ the \ base \ 10|\)
\(lg (x ^ lg (x)) = lg (100x)\)
\(lg ^ 2 (x) = 2 + lgx\)
\(lg 2 ^ x-lg x -2 = 0\)
\(lg x = 2 x = 100\)
\(lg x = -1 x = \dfrac{1}{10} = 0.1\)