CA Foundation · Quantitative Aptitude · Ratio and Proportion, Indices and Logarithms
The value of (log₂ 9) × (log₃ 8) is:
The value is 6. Write log₂ 9 as 2·log₂ 3 and log₃ 8 as 3·log₃ 2. Because log₂ 3 × log₃ 2 equals 1 by the change of base rule, the product is 2 × 3 × 1 = 6.
- A6Correct
- B12
- C72
- D5
Explanation
log₂ 9 = 2 log₂ 3 and log₃ 8 = 3 log₃ 2. Their product = 6 × (log₂ 3 × log₃ 2) = 6 × 1 = 6. The option 12 arises from forgetting that log₂3 × log₃2 = 1 and mishandling the powers.
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 ratio compounded of 2:3, 9:4 and 5:6 is:
- The third proportional to 8 and 12 is:
- The ratio of the ages of a father and son is 7 : 2. If componendo and dividendo is applied, the ratio (father + son) : (father − son) equals…
- If 3^(x+2) = 243, then the value of x is:
- If log₁₀ 2 = 0.3010, then the number of digits in 2^40 is:
- If log₃ (x − 2) + log₃ (x + 6) = 2, then the value of x is: