21.
$$\eqalign{ & {\text{If }}{\log _{1000}}x = - \frac{1}{4}{\text{, }} \cr & {\text{then the value of }}x{\text{ is = ? }} \cr} $$

22.
$$\frac{{\log \sqrt 8 }}{{\log 8}}\,\,{\text{is equal to = ?}}$$

23.
$$\eqalign{ & {\text{The value of }} \cr & \,\frac{{6{\text{ }}{{\log }_{10}}1000}}{{3{\text{ }}{{\log }_{10}}100}}\,\,{\text{is equal to - }} \cr} $$

24.
$$\eqalign{ & {\text{If }}{\log _2}\left[ {{\text{ }}{{\log }_3}\left( {{\text{ }}{{\log }_2}x} \right)} \right] = 1, \cr & {\text{then }}x\,\,{\text{is equal to = ?}} \cr} $$

25.
What is the value of the following expression? $$\log \left( {\frac{8}{{14}}} \right) - \log \left( {\frac{{15}}{{16}}} \right) + \log \left( {\frac{{35}}{{24}}} \right)$$