Question

X^lg(x)=100^x find x

Answer 1

$x^lg(x)=100^x$

$X^lg(x)=100^x:x$  $|Solve \ for \ x|$

$|Use \ logarithms \ of \ both \ sides \ of \ the \ base \ 10|$

$lg (x ^ lg (x)) = lg (100x)$

$lg ^ 2 (x) = 2 + lgx$

$lg 2 ^ x-lg x -2 = 0$

$lg x = 2 x = 100$

$lg x = -1 x = \dfrac{1}{10} = 0.1$