Multiple choice general knowledge math & puzzles

log27 /log 12 = a then log 16 /log 6 = ?

  1. 4(3+a)/(3-a)

  2. 2(3+a)/(3-a)

  3. 8(3+a)/(3-a)

  4. 4(3-a)/(3+a)
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Given log27/log12 = a, we know log27 = log(3^3) = 3log3, and log12 = log(3×4) = log3 + log4 = log3 + 2log2. We need log16/log6 = log(2^4)/log(2×3) = 4log2/(log2+log3). Substituting and simplifying using the given ratio yields the answer 4(3-a)/(3+a). This requires logarithmic properties and algebraic manipulation.

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