Question

Number of real solutions of the equation `log_10(-x) = sqrt(log_10sqrt(x^2))`?

Answer 1

See below.

Explanation:

`sqrt(x^2) = abs x` then

`log_10 (-x) = sqrt(log_10 absx)` now calling `y = -x`

`log_10 y = sqrt(log_10 abs y)` has sense only for `y= 1` or `y = 10`

then the solutions are for

`x = {-1, -10}`