Question

The sum of all values of $x$ satisfying the equation $\log _{0.03}\left(\left(\log _2 x\right)^3-4\left(\log _2 x\right)^2+3\left(\log _2 x\right)+1\right)=0$, is

• A. 16
• B. 15
• C. 10
• D. 11

Answer 1

Answer: (D)

Put$ \log _2 x = t \Rightarrow t ^3-4 t ^2+3 t =0$
$\Rightarrow t \left( t ^2-4 t +3\right)=0$
$\Rightarrow t ( t -1)( t -3)=0 \Rightarrow t =0,1,3$
$\therefore \log _2 x =0,1,3$
$\Rightarrow x =1,2,8 \Rightarrow sum =11 $