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What is the value of x satisfying the equation (frac{4^{2x}}{4^{3x}}) = 2?

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

Correct Answer: Option B

Explanation

(frac{4^{2x}}{4^{3x}}) = 2
4^{2x – 3x} = 2
4^-x = 2
(2²)^-x
= 2¹
Equating coefficients: -2x = 1
x = -(frac{1}{2})