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Given that \(\frac{1}{8^{2-3y}}\)  = 2\(^{y + 2}\), find y.

Further Mathematics
WAEC 2025

Given that \(\frac{1}{8^{2-3y}}\)  = 2\(^{y + 2}\), find y.

  • A. 1
  • B. \(\frac{1}{5}\)
  • C. \(\frac{7}{8}\)
  • D. \(\frac{1 1}{5}\)
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Correct Answer: Option A
Explanation

\(\frac{1}{8^{2-3y}}\)  = 2\(^{y + 2}\)

8\(^{-1(2 - 3y)}\) = 2\(^{y + 2}\)

2\(^{3(-2 + 3y)}\) = 2\(^{y + 2}\)

-6 + 9y = y + 2

9y - y = 2 + 6

8y = 8

y = \(\frac{8}{8}\) = 1


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