Question

If ${\log }_{2006}\left({\log }_{2007}x\right)<0$, then find the interval in which $x$ lies.

• A. $x\in (1,2007)$
• B. $x\in (2,2007)$
• C. $x\in (1,207)$
• D. None of these

Answer 1

Answer: (A)

$x\in (1,2007)$

${\log }_{2006}\left({\log }_{2007}\right(x\left)\right)<0$

$\Rightarrow {\log }_{2007}\left(x\right)>0$

$\Rightarrow x>(2007{)}^0$

$\Rightarrow x>1$

Also ${\log }_{2007}\left(x\right)<(2008{)}^0$

$\Rightarrow {\log }_{2007}x<1$

$\Rightarrow x<2007$

$\therefore x\in (1,2007)$