Question

If \( \log_3 2 \), \( \log_3 (2^x - 5) \), and \( \log_3 \left( \frac{2^x - 7}{2} \right) \) are in AP, then \( x \) is equal to

• A. \( 1, \frac{1}{2} \)
• B. \( 1, \frac{1}{3} \)
• C. \( 1, \frac{3}{2} \)
• D. None of these

Hint:

When solving logarithmic equations, use logarithmic properties to simplify and then exponentiate both sides to eliminate the logarithms.

Answer 1

The Correct Option is D