If \(\frac{1}{5^{-y}} = 25(5^{4-2y})\), find the value of y.
- 4
-
2
- -4
- -5
The correct answer is: B
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
\(y = 6 - 2y\)
\(3y = 6 \implies y = 2\)