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

Answer: (D)

a

Answer 2

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:
$log_6\ ​G=a$