Number of solutions of the equation `ln|x| = ||x|-2|.`

Let [ ] represents the greatest integer function and [ x^3 + x^2 + 1 + x] = [ x^3 + x^2 + 1] + x. The number of solution of the equation log|[x]| = 2 - |[x ]|

The number of solutions of the equation 3"log"_(3)|-x| = "log"_(3) x^(2), is

The number of solutions of the equation 3"log"_(3)|-x| = "log"_(3) x^(2), is

The number of solutions of the equation e ^(x) - log |x|=0 is :

The number of solutions of the equation e ^(x) - log |x|=0 is :

If log_(a)(1-sqrt(1+x))=log_(a^(2))(3-sqrt(1+x)) then the number of solutions of the equation is

Total number of solutions of the equation sin pi x=|ln_(e)|x|| is :

The number of real solutions of the equation log_(05)x=|x| , is