Question

If \(log_a\) \(30\) = \(A\), \(log_a\) \(\bigg(\frac{5}{3}\bigg)\) = \(-B\) and \(log_2\; a\) = \(\frac{1}{3}\), then \(log_3\) \(a\) equals.

• A. \(\frac{2}{A+B}-3\)
• B. \(\frac{A+B-3}{2}\)
• C. \(\frac{2}{A+B-3}\)
• D. \(\frac{A+B}{2}-3\)

Answer 1

The Correct Option is C

The correct answer is (C): \(\frac{2}{A+B-3}\)

\(log_a\;5+log_a\;3+log_a\;2 = A\)

\(log_a\;5+log_a\;3 = A-3\)

But \(log_a\;5-log_a\;3 = -B\)

Hence \(2\;log_a\;3 = A+B-3\)

\(log_3\;a = \frac{2}{A+B-3}\)