If (16^{3x} = frac{1}{4}(32^{x – 1})), find the value of x.
-
A.
(-1) -
B.
(frac{-1}{3}) -
C.
(frac{-3}{7}) -
D.
(frac{-5}{19})
Correct Answer: Option A
Explanation
(16^{3x} = frac{1}{4}(32^{x – 1}))
((2^{4})^{3x} = (2^{-2})((2^{5})^{x – 1}))
(2^{12x} = 2^{-2 + 5x – 5})
(12x = -7 + 5x)
(7x = -7 implies x = -1)