Solve: (4(2^{x^2}) = 8^{x})
-
A.
(1, 2) -
B.
(1, -2) -
C.
(-1, 2) -
D.
(-1, -2)
Correct Answer: Option A
Explanation
(4(2^{x^2}) = 8^{x} equiv (2^{2})(2^{x^2}) = (2^{3})^{x})
(implies 2^{2 + x^{2}} = 2^{3x})
Comparing bases, we have
(2 + x^{2} = 3x implies x^{2} – 3x + 2 = 0)
(x^{2} – 2x – x + 2 = 0 )
(x(x – 2) – 1(x – 2) = 0)
((x – 1) = 0) or ((x – 2) = 0)
(x = text{1 or 2})