If \(\frac{1}{5^{-y}} = 25(5^{4-2y})\), find the value of y.
FURTHER MATHEMATICS
WAEC 2014
If \(\frac{1}{5^{-y}} = 25(5^{4-2y})\), find the value of y.
- A. 4
- B. 2
- C. -4
- D. -5
Correct Answer: B. 2
Explanation
\(\frac{1}{5^{-y}} = 25(5^{4-2y})\)
\(\implies 5^{y} = (5^{2})(5^{4-2y})\)
\(5^{y} = 5^{2+4-2y}\)
Comparing bases, we have
\(y = 6 - 2y\)
\(3y = 6 \implies y = 2\)
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