Question
What is the value of the following expression?
$$\log \left( {\frac{9}{{14}}} \right) - $$ $$\log \left( {\frac{{15}}{{16}}} \right) + $$ $$\log \left( {\frac{{35}}{{24}}} \right)$$
$$\log \left( {\frac{9}{{14}}} \right) - $$ $$\log \left( {\frac{{15}}{{16}}} \right) + $$ $$\log \left( {\frac{{35}}{{24}}} \right)$$
Answer: Option A
$$\eqalign{
& \log \left( {\frac{9}{{14}}} \right) - \log \left( {\frac{{15}}{{16}}} \right) + \log \left( {\frac{{35}}{{24}}} \right) \cr
& = \log \left( {\frac{9}{{14}} \div \frac{{15}}{{16}} \times \frac{{35}}{{24}}} \right) \cr
& = \log \left( {\frac{9}{{14}} \times \frac{{16}}{{15}} \times \frac{{35}}{{24}}} \right) \cr
& = \log 1 \cr
& = 0 \cr} $$
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$$\eqalign{
& \log \left( {\frac{9}{{14}}} \right) - \log \left( {\frac{{15}}{{16}}} \right) + \log \left( {\frac{{35}}{{24}}} \right) \cr
& = \log \left( {\frac{9}{{14}} \div \frac{{15}}{{16}} \times \frac{{35}}{{24}}} \right) \cr
& = \log \left( {\frac{9}{{14}} \times \frac{{16}}{{15}} \times \frac{{35}}{{24}}} \right) \cr
& = \log 1 \cr
& = 0 \cr} $$
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