Solve (9^{2x + 1} = 81^{3x + 2})
-
A.
(frac{-3}{4}) -
B.
(frac{-2}{3}) -
C.
(frac{4}{5}) -
D.
(frac{3}{2})
Correct Answer: Option A
Explanation
(9^{2x + 1} = 81^{3x + 2})
(9^{2x + 1} = (9^{2})^{3x + 2})
(9^{2x + 1} = 9^{6x + 4})
Equating powers,
(2x + 1 = 6x + 4 implies -3 = 4x)
(therefore x = frac{-3}{4})