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If log\(_{10}\)2 = 0.3010 and log\(_{10}\)3 = 0.4771, simplify: (Log\(_{10}\)8-log\(_{10}\)2) ÷ (Log\(_{10}\)9 - log\(_{10}\)2)

Mathematics
NECO 2004

If log\(_{10}\)2 = 0.3010 and log\(_{10}\)3 = 0.4771, simplify: (Log\(_{10}\)8-log\(_{10}\)2) ÷ (Log\(_{10}\)9 - log\(_{10}\)2)

  • A. 4
  • B. 3
  • C. -0.92
  • D. -4
  • E. 0.92
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Correct Answer: Option E
Explanation

\(\frac{\log 8 - \log 2}{\log 9 - \log 2} = \frac{2\log 2}{2\log 3 - \log 2}\)

Numerator: \(2 \times 0.3010 = 0.6020\)

Denominator: \(2 \times 0.4771 - 0.3010 = 0.6532\)

\(\frac{0.6020}{0.6532} = \mathbf{0.92}\)


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