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Let S_n(x) = log_(a/2) x + log_(a/3) x + log_(a/4) x + log_(a/11) x + log_(a/18) x + log_(a/27) x + .... Up to n-terms, where a > 1. If S_24(x) = 1093 and S_12(2x) = 265, then value of a is equal to _____.

1. 2
2. 3
3. 4
4. 5

Correct answer: 2

Solution

The correct option is 2 because the logarithmic terms in S_n(x) can be expressed in a consistent base, and the given values for S_24(x) and S_12(2x) can be solved simultaneously to reveal that a must equal 2 for the equations to hold true.

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