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If 2 log x (3\(\frac{3}{8}\)) = 6, find the value of x

Mathematics
WAEC 2013

If 2 log x (3\(\frac{3}{8}\)) = 6, find the value of x
  • A. \(\frac{3}{2}\)
  • B. \(\frac{4}{3}\)
  • C. \(\frac{2}{3}\)
  • D. \(\frac{1}{2}\)
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Correct Answer: Option A
Explanation
2 log x (3\(\frac{3}{8}\)) = 6(divide both sides by 2)

\(\frac{2 log_x(3 \frac{3}{8})}{2} = \frac{6}{2}\)

\(\log_x \frac{27}{8} = 3\)

\(\frac{27}{8} = x^3\)

\(x^3 = \frac{27}{8}\)

x = \(\sqrt{\frac{27}{8}}\)

= (\(\frac{27}{8}\))\(\frac{1}{3}\)

= \(\frac{(3^3)^{\frac{1}{3}}}{(2^3)^{\frac{1}{3}}}\)

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

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