Solve ` sqrt(log(-x)) = log sqrt(x^(2)) `(base is 10).

Explanation

Since the equation can be satisfied only for ` x lt 0`, we have ` sqrt(x^(2)) = |x| =- x`.
So, givne equation reduces to
` sqrt(log(-x))= log(-x)`
` or log(-x) = [log(-x)]^(2)`
` or log(-x)[1-log(-x)]=0`
if ` log(-x) =0 rArr -x=1 rArr x =- 1`
if ` log_(10)(-x)=1 rArr -x=10 rArr x =- 10`