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