Question

If ${\log }_3\left({\log }_{2}x\right)+{\log }_{1/3}\left({\log }_{1/2}x\right)=1$ then $x$ equals

• A. $4$
• B. $8$
• C. $16$
• D. There is no solution
  

Answer 1

The correct option is D There is no solution

${\log }_3\left({\log }_{2}x\right)+{\log }_{1/3}\left({\log }_{1/2}x\right)=1$
$\Rightarrow {\log }_3\left({\log }_{2}x\right)-{\log }_3\left({\log }_2\frac{1}{x}\right)=1$
$\Rightarrow {\log }_3(-1)=1$
But we know log of negative number is not defined.
Hence there is no solution