Evaluate \(\log_{0.25} 8\)

FURTHER MATHEMATICS
WAEC 2006

Evaluate \(\log_{0.25} 8\)

  • A. \(\frac{3}{2}\)
  • B. \(\frac{2}{3}\)
  • C. \(-\frac{2}{3}\)
  • D. \(-\frac{3}{2}\)

Correct Answer: D. \(-\frac{3}{2}\)

Explanation

\(\log_{0.25} 8 = x\)

\(8 = 0.25^{x}\)

\(2^{3} = (2^{-2})^{x} \implies 3 = -2x\)

\(x = -\frac{3}{2}\)



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