What is the value of the following expression?
$$\log \left( {\frac{9}{{14}}} \right) - $$   $$\log \left( {\frac{{15}}{{16}}} \right) + $$   $$\log \left( {\frac{{35}}{{24}}} \right)$$

Solution (By Examveda Team)

$$\eqalign{ & \log \left( {\frac{9}{{14}}} \right) - \log \left( {\frac{{15}}{{16}}} \right) + \log \left( {\frac{{35}}{{24}}} \right) \cr & = \log \left( {\frac{9}{{14}} \div \frac{{15}}{{16}} \times \frac{{35}}{{24}}} \right) \cr & = \log \left( {\frac{9}{{14}} \times \frac{{16}}{{15}} \times \frac{{35}}{{24}}} \right) \cr & = \log 1 \cr & = 0 \cr} $$