Question

Suppose, \(log_3 \ x = log_{12} \ y = a\), where x, y are positive numbers. If G is the geometric mean of x and y, and \(log_6\) G is equal to

• A. \(\sqrt{a}\)
• B. 2a
• C. \(\frac{a}{2}\)
• D. a

Answer 1

The Correct Option is D

The logarithmic expressions can be rewritten as follows:
\(log_3​\ x=a⟹x=3^a\)
\(log_12\ ​y=a⟹y=12^a\)
Therefore, when multiplying these expressions:
\(xy=36^a\)
And since \(xy=G=6^a\), it follows that:
\(log_6\ ​G=a\)