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NECO 2023 · Paper 1 · Q7

If log⁡103=0.4771\log_{10}3 = 0.4771, evaluate log⁡108.1\log_{10}8.1.

Worked solution (try it first)
  1. Write 8.1 using 3 and 10: 8.1=8110=34108.1 = \frac{81}{10} = \frac{3^4}{10}.
  2. So log⁡8.1=4log⁡3−log⁡10\log 8.1 = 4\log 3 - \log 10
    =4log⁡3−1= 4\log 3 - 1.
  3. That is 4(0.4771)−1=1.9084−1=0.90844(0.4771) - 1 = 1.9084 - 1 = 0.9084, option D.

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