CA Foundation · Quantitative Aptitude · Ratio and Proportion, Indices and Logarithms
Given log₁₀ 2 = 0.3010, the number of digits in 2²⁰ is:
2²⁰ has 7 digits. Its logarithm is 20 × 0.3010 = 6.020, whose characteristic is 6, and the number of digits equals the characteristic plus one, giving 7. This matches 2²⁰ = 1,048,576.
- A7Correct
- B6
- C8
- D5
Explanation
log₁₀ 2²⁰ = 20 × 0.3010 = 6.020. The characteristic is 6, so the number of digits is 6 + 1 = 7. Answering 6 mistakes the characteristic for the digit count. Indeed 2²⁰ = 1,048,576, which has 7 digits.
Did you get it right without looking?
One question tells you little. A timed set on Ratio and Proportion, Indices and Logarithms shows your real accuracy, how long you take and where you lose marks.
More Ratio and Proportion, Indices and Logarithms questions
- The value of (2³ × 2⁵) ÷ 2⁴ is:
- If x = 4ab/(a + b), with a ≠ b and a, b ≠ 0, then the value of (x + 2a)/(x − 2a) + (x + 2b)/(x − 2b) is:
- If log₁₀ 2 = 0.3010, the number of digits in 2⁴⁰ is:
- If log₁₀ 2 = 0.3010, the value of log₁₀ 5 is:
- A mixture of 60 litres contains milk and water in the ratio 7 : 3. How many litres of water must be added so that the ratio of milk to water…
- If the sub-duplicate ratio of x : 25 is equal to 3 : 5, then x equals: