What is the value of x satisfying the equation \(\frac{4^{2x}}{4^{3x}}\) = 2?
A
-2
B
-\(\frac{1}{2}\)
C
\(\frac{1}{2}\)
D
2
Verified Correct Answer: B.
Step-by-Step Mathematical Solution
\(\frac{4^{2x}}{4^{3x}}\) = 2
42x - 3x = 2
4-x = 2
(22)-x
= 21
Equating coefficients: -2x = 1
x = -\(\frac{1}{2}\)
Source: Myschool Past Questions Archive (Record #31294)