If (frac{1}{5^{-y}} = 25(5^{4-2y})), find the value of y.
-
A.
4 -
B.
2 -
C.
-4 -
D.
-5
Correct Answer: Option 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)