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