the no of sols of da eq

\(log_x5)³ - (log_x5)² -12log _x^1/25 =0 are

a)3        B)2     c)0        D)infinite

(log_x5)³ - (log_x5)² -12log _x^1/25 =0

put log₅ x = y

so we get :  1/y^3 - 1/y^2 -24/y=0

now y cant b zero so :

1- y - 24y^2=0

or, 24y^2 + y-1=0

now for the abv quad eqn the discriminant >0 ..so it has two solns ..

hence x too has two solns...