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CA Foundation · Quantitative Aptitude · Ratio and Proportion, Indices and Logarithms

If log₁₀ x = 2 log₁₀ 6 − 3 log₁₀ 2 + log₁₀ 10, then x equals:

x equals 45. Applying the power law gives log 36 minus log 8 plus log 10, and combining with the product and quotient laws yields log of 36 times 10 divided by 8, which is log 45, so x is 45.

  1. A45Correct
  2. B30
  3. C60
  4. D36

Explanation

Using power law: 2 log 6 = log 36 and 3 log 2 = log 8. So log x = log 36 − log 8 + log 10 = log (36 × 10 / 8) = log 45. Hence x = 45. If one forgets the log 10 term, x = 4.5; using 36/8 alone is wrong.

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