Logarithmic Relation and Geometric Mean

CAT 2017 Slot 1 · Quantitative Ability · Hard · Exponents and Logarithms

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

Answer

$x = 3^a$ and $y = 12^a$ . Geometric mean $G = \sqrt{xy} = \sqrt{3^a \cdot 12^a} = \sqrt{36^a} = 6^a$ . $\log_6 G = \log_6 (6^a) = a$ .

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