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 = (1)/(10) = 0.1`