If \(16^{3x} = \frac{1}{4}(32^{x - 1})\), find the value of x.
FURTHER MATHEMATICS
WAEC 2010
If \(16^{3x} = \frac{1}{4}(32^{x - 1})\), find the value of x.
- A. \(-1\)
- B. \(\frac{-1}{3}\)
- C. \(\frac{-3}{7}\)
- D. \(\frac{-5}{19}\)
Correct Answer: A. \(-1\)
Explanation
\(16^{3x} = \frac{1}{4}(32^{x - 1})\)
\((2^{4})^{3x} = (2^{-2})((2^{5})^{x - 1})\)
\(2^{12x} = 2^{-2 + 5x - 5}\)
\(12x = -7 + 5x\)
\(7x = -7 \implies x = -1\)
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