CDS 2026 · PYQ · Logarithms · medium
If log₁₀(80) = p, log₁₀(45) = q and log₁₀(216) = r, then what is log₁₀(384) equal to?
- A.p + q + r
- B.p - q + r✓ Correct
- C.p - q - r
- D.p + q - r
80 = 2⁴·5, 45 = 3²·5, 216 = 2³·3³, 384 = 2⁷·3. Compute p - q + r = log(80) - log(45) + log(216) = log(80·216/45). Now 80·216/45 = 17280/45 = 384. So log₁₀(384) = p - q + r.
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