Question

If 2^{m – 1} + 2^{m + 1} = 640, then find m

Answer 1

Given 2^{m – 1} + 2^{m + 1} = 640

2^{m – 1} + 2^{m + 1} = 128 + 512

2^{m – 1} + 2^{m + 1} = 2⁷ + 2⁹

m – 1 = 7

m = 7 + 1

m = 8 ...[consecutive powers of 2]

Powers of 2:

2, 4, 8, 16, 32, 64, 128, 256, 512, ….