CMA Foundation · Fundamentals of Business Mathematics and Statistics · Indices and Logarithms
If log x to base 4 equals 2.5, what is the value of x?
The value of x is 32. Converting the logarithm to exponential form gives x equal to 4 raised to 2.5, which is 4 squared (16) multiplied by the square root of 4 (2), giving 32.
- A10
- B16
- C32Correct
- D64
Explanation
x = 4^2.5 = 4^2 x 4^0.5 = 16 x 2 = 32. Check: log4 32 = log2 32 / log2 4 = 5/2 = 2.5. The option 64 comes from taking 4^3, and 10 from multiplying 4 by 2.5.
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