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If 9\(^{(x - \frac{1}{2})} = 3^{x^2}\) Find the value of x

Mathematics
JAMB 1993

If 9\(^{(x - \frac{1}{2})} = 3^{x^2}\) Find the value of x

  • A. \(\frac{1}{2}\)
  • B. 1
  • C. 2
  • D. 3
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Correct Answer: Option B
Explanation

9(x - \(\frac{1}{2}\)) 3x2 = 3\(^{2(x - \frac{1}{2})}\) = 3\(^x{^2}\)
∴ 2(x - \(\frac{1}{2}\)) = x2

2x - 1 = x\(^2\)

hence x\(^2\) - 2x + 1 = 0

(x - 1)(x - 1) = 0

x = 1


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