CMA Foundation · Fundamentals of Business Mathematics and Statistics · Indices and Logarithms
If log10(N) = 2.6021 and log10(2) = 0.3010, then the number N is closest to which value? (Use 10^0.3010 = 2 and 10^0.3011 ≈ 2)
N is 400. The mantissa 0.6021 equals twice log 2, which is log 4, and the characteristic 2 contributes a factor of 10². So N = 4 × 100 = 400. The characteristic of 2 shows the number has three digits before the decimal point.
- A40
- B400Correct
- C4000
- D4.0
Explanation
2.6021 = 2 + 0.6021 and 0.6021 = 2 × 0.3010 = log 4. So N = 4 × 10^2 = 400. Option 40 results from using characteristic 1, and 4000 from characteristic 3.
Did you get it right without looking?
One question tells you little. A timed set on Indices and Logarithms shows your real accuracy, how long you take and where you lose marks.
More Indices and Logarithms questions
- Given log 2 = 0.3010, how many digits are there in the integral part of 2^40?
- If log 6.4 = 0.8062, what is the logarithm of 0.0064 written as characteristic and mantissa?
- Simplify: (27)^(2/3) × (16)^(-1/4) ÷ (9)^(1/2).
- Given log10(3) = 0.4771, the value of log10(0.0003) is written in the bar form as:
- What is the characteristic of log10 (0.00362)?
- Given log10(2) = 0.3010, what is the characteristic of log10(2000)?