CAT 2017 Logarithms Question (Medium)

Question

Suppose, , where are positive numbers. If is the geometric mean of and , and is equal to

Accepted Answer

Step 1 We are given log_ 3 x a log_ 12 y a We need to find log_ 6 G where is the geometric mean of and G Step 2 From , we have x 3 a From , we have y 12 a Thus G Since , we have G 6 a Step 3 Now log_ 6 G log_ 6 6 a a Final Answer Option D a

CAT 2017

Quantitative

Logarithms

Medium

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:

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