If 2x - 1 + 2x + 1 = 2560, find the value of x.

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If 2^{x - 1} + 2^{x + 1} = 2560, find the value of x.

1. 10
2. 12
3. 9
4. 8
5. None of the above

Correct Option: A

2^{x - 1} + 2^{x + 1} = 2560
2^{x - 1} + 2^{x - 1 + 2} = 2560
Apply the Law of Algebra
2^{x - 1} + 2^{x - 1} x 2² = 2560
⇒ 2^{x - 1} ( 1 + 2² ) = 2560
⇒ 2^{x - 1} = 2560/5 = 512 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2
⇒ 2^{x - 1} = 2⁹
⇒ x - 1 = 9
∴ x = 9 + 1 = 10