For `a >0,!=1,`the roots of the equation `(log)_(a x)a+(log)_x a^2+(log)_(a^2a)a^3=0`are given`a^(-4/3)`(b) `a^(-3/4)`(c) `a`(d) `a^(-1/2)`A. `a^(-4//3)`B. `a^(-3//4)`C. aD. `a^(-1//2)`

For `a >0,!=1,`the roots of the equation `(log)_(a x)a+(log)_x a^2+(lo

1.	For `a >0,!=1,`the roots of the equation `(log)_(a x)a+(log)_x a^2+(log)_(a^2a)a^3=0`are given`a^(-4/3)`(b) `a^(-3/4)`(c) `a`(d) `a^(-1/2)`A. `a^(-4//3)`B. `a^(-3//4)`C. aD. `a^(-1//2)`
Answer» Correct Answer - A::D ` log_(ax)a+log_(x)a^(2)+log_(a^(2)x)a^(3) = 0` ` or 1/(log_(a)ax)+2/(log_(a)x)+3/((log_(a)a^(2)x))= 0` `or 1/(1+log_(a)x) + 2/(log_(a) x) + 3/((2+log_(a)x )) = 0` Let ` log_(a)x = y ," we have" 1/(y+1) + 2/y+3/(2+y) = 0` ` or 6y^(2) + 11y+4 = 0` ` or y = log_(a) x = - 1/2, - 4/3` ` rArr x = a^(-4//3), a^(-1//2)`