Question

\(log_xb-log_xa=log_xc-log_xb\)  \(∴ac=\)

• A. \(a^2\)
• B. \(b^2\)
• C. \(c^2\)
• D. None

Answer 1

The Correct Option is B

To solve this problem, we need to simplify the given logarithmic equation:

1. Given Equation:
\( \log_x b - \log_x a = \log_x c - \log_x b \)

2. Applying Logarithmic Properties:
Using the property \( \log_x p - \log_x q = \log_x \left(\frac{p}{q}\right) \), we can rewrite the equation as:

\( \log_x \left(\frac{b}{a}\right) = \log_x \left(\frac{c}{b}\right) \)

3. Equating the Arguments:
Since the logarithms are equal, their arguments must be equal as well. Therefore:

\( \frac{b}{a} = \frac{c}{b} \)

4. Solving for \( ac \):
Cross multiplying the equation gives:

\( b^2 = ac \)

Final Answer:
The correct option is (B) \( b^2 \).