If 2 x - 1 + 2 x + 1 = 320, then find the value of x ?

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If 2 ^{x - 1} + 2 ^{x + 1} = 320, then find the value of x ?

1. 6
2. 8
3. 7
4. 5

Correct Option: C

∵ 2^{x - 1} + 2^{x + 1} = 320
Apply the law of Algebra
⇒ 2^{x - 1}(1 + 2² ) = 320
⇒ 2^{x - 1}(1 + 4 ) = 320
⇒ 2^{x - 1} x 5 = 320
⇒ 2^{x - 1} = 64 = 2 x 2 x 2 x 2 x 2 x 2
⇒ 2^{x - 1} = 2⁶
if p^X = p^Y then X will be equal to Y. means X = Y;
⇒ x - 1 = 6
∴ x = 7