Question

The value of \( x (\log y - \log z) \times y (\log z - \log x) \) is equal to:

• A. 0
• B. 3
• C. 5
• D. 1

Hint:

Use logarithmic properties such as \( \log a - \log b = \log \left( \frac{a}{b} \right) \) to simplify expressions involving logarithms.

Answer 1

The Correct Option is A

We start with the expression \( x (\log y - \log z) \times y (\log z - \log x) \). Applying logarithmic properties: \[\n\log a - \log b = \log \left( \frac{a}{b} \right)\n\] This transforms the expression into: \[\nx \log \left( \frac{y}{z} \right) \times y \log \left( \frac{z}{x} \right)\n\] Multiplying terms yields: \[\nx \cdot y \cdot \log \left( \frac{y}{z} \right) \cdot \log \left( \frac{z}{x} \right)\n\] The simplified expression equals 0. Therefore, the answer is 0.