CMA Foundation · Fundamentals of Business Mathematics and Statistics · Indices and Logarithms
If log base x of 0.0625 = -4, what is the value of x?
The value of x is 2. The definition of a logarithm gives x raised to minus 4 equals 0.0625, which is 1/16. Therefore x to the fourth power is 16, so the positive base is 2, and 2 to the minus 4 does equal 0.0625.
- A2Correct
- B4
- C1/2
- D16
Explanation
By definition x^(-4) = 0.0625 = 1/16. So x^4 = 16, giving x = 2 (the base must be positive). Check: 2^(-4) = 1/16 = 0.0625. The option 4 results from solving x^2 = 16, and 1/2 from ignoring the negative sign of the exponent.
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