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If \(\log_{10}y + 3\log_{10}x \geq \log_{10}x\), express y in terms of x.

Further Mathematics
WAEC 2016

If \(\log_{10}y + 3\log_{10}x \geq \log_{10}x\), express y in terms of x.

  • A. \(y \geq \frac{1}{x}\)
  • B. \(y \leq \frac{1}{x}\)
  • C. \(y \leq \frac{1}{x^{2}}\)
  • D. \(y \geq \frac{1}{x^{2}}\)
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Correct Answer: Option D
Explanation

\(\log_{10}y + 3\log_{10}x \geq \log_{10}x\)

\(\implies \log_{10}y \geq \log_{10}x - 3 \log_{10}x \)

\(\log_{10}y \geq -2\log_{10}x = \log_{10}y \geq \log_{10}x^{-2}\)

\(\log_{10}y \geq \log_{10}(\frac{1}{x^{2}}) \implies y \geq \frac{1}{x^{2}}\)


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JAMB CBT Mobile App 2025 - Free Download
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