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

Applying the logarithmic property \( \log a - \log b = \log \frac{a}{b} \), we simplify:\n\[\n\log \frac{14}{15} - \log \frac{3}{25} - \log \frac{7}{9} = \log \left( \frac{14}{15} \times \frac{25}{3} \times \frac{9}{7} \right)\n\]\nSimplification:\n\[\n\frac{14}{15} \times \frac{25}{3} \times \frac{9}{7} = \frac{14 \times 25 \times 9}{15 \times 3 \times 7} = \frac{3150}{3150} = 1\n\]\nThis gives \( \log 1 = 0 \). The answer is 0.