Multiple choice

The sum of the series log 3 + log 9/4 + log 27/16 + log 81/64 + …up to 10 terms is

  1. 55 log 3 - 110 log 2

  2. 5(11 log 3 - 9 log 4)

  3. 55 log 3 - 11 log 32

  4. 1

  5. None of these
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B Correct answer
AI explanation

Using the product rule of logarithms, log 3 + log 9/4 + log 27/16 + log 81/64 sums to log(3 * 9/4 * 27/16 * 81/64 up to 10 terms). The product of these 10 terms forms a geometric progression with the first term 3 and common ratio 3/4, which calculates to 55 log 3 - 45 log 4. This expression equals 5(11 log 3 - 9 log 4).

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