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CMA Foundation · Fundamentals of Business Mathematics and Statistics · Indices and Logarithms

If 3^x = 81 × 27, find x using logarithms of base 3 properties.

Since 81 is 3 to the power 4 and 27 is 3 to the power 3, their product is 3 to the power 7, so x equals 7.

  1. A7Correct
  2. B12
  3. C5
  4. D9

Explanation

81 = 3^4 and 27 = 3^3, so 81 × 27 = 3^7. Hence x = 7. Option 12 results from multiplying the exponents (4 × 3) instead of adding.

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