CDS 2026 (I) Elementary Mathematics, question 29

Topic: Algebra

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Q29

If log⁡10(80)=p\log_{10}(80)=p, log⁡10(45)=q\log_{10}(45)=q and log⁡10(216)=r\log_{10}(216)=r, then what is log⁡10(384)\log_{10}(384) equal to ?

  1. (a) p+q+rp+q+r
  2. (b) p−q+rp-q+rCorrect answer
  3. (c) p−q−rp-q-r
  4. (d) p+q−rp+q-r

Solution.

Answer: (b) p−q+rp-q+r

  1. Combine the supplied logarithms by matching their arguments: 80×216/45=38480 \times 216/45 = 384.
  2. Therefore log⁡10384=log⁡1080−log⁡1045+log⁡10216\log_{10}384 = \log_{10}80 - \log_{10}45 + \log_{10}216.