Question

The value of \( \log \frac{14}{15} - \log \frac{3}{25} - \log \frac{7}{9} \) is:

• A. 2
• B. 3
• C. 0
• D. 1

Hint:

Use the properties of logarithms to combine multiple terms and simplify the expression before evaluating it.

Answer 1

The Correct Option is C

Using the logarithmic property \( \log a - \log b = \log \frac{a}{b} \), we can simplify the expression: \[ \log \frac{14}{15} - \log \frac{3}{25} - \log \frac{7}{9} = \log \left( \frac{14}{15} \times \frac{25}{3} \times \frac{9}{7} \right) \] Simplifying inside the logarithm: \[ \frac{14}{15} \times \frac{25}{3} \times \frac{9}{7} = \frac{14 \times 25 \times 9}{15 \times 3 \times 7} = \frac{3150}{3150} = 1 \] Thus, the expression becomes \( \log 1 = 0 \). Therefore, the correct answer is 0.