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If 2^{x–1} + 2^{x+1} = 320, then x equals

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If 2x–1 + 2x+1 = 320, then x equals

(a) 4

(b) 5

(c) 6

(d) 7

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1 Answer

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Best answer

Correct option is (d) 7

2x−1 + 2x+1 = 320

If x = 4 then

24 − 1 + 24 + 1 = 320

23 + 25 = 320

40 \(\ne\) 320

If x = 5 then

25 − 1 + 25 + 1 = 320

24 + 26 = 320

80 \(\ne\) 320

If x = 6 then

26 − 1 + 26 + 1 = 320

25 + 27 = 320

160 \(\ne\) 320

If x = 7 then

27 − 1 + 27 + 1 = 320

26 + 28 = 320

320 = 320

Hence x = 7

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