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

If 3^(2x-1) = 81, the value of x is:

x equals 5/2. Writing 81 as 3^4 lets us equate the exponents, so 2x - 1 = 4, which gives 2x = 5 and x = 5/2. Substituting back gives 3^4 = 81, confirming the result.

  1. A2
  2. B5/2Correct
  3. C3
  4. D5

Explanation

81 = 3^4, so 2x-1 = 4, giving 2x = 5 and x = 5/2. Check: 2(5/2)-1 = 4, and 3^4 = 81. Choosing x = 2 comes from setting 2x = 4 and forgetting the -1; x = 3 comes from treating 2x-1 as 5.

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