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प्रश्न
If 2n+2 – 2n+1 + 2n = c × 2n, find the value of c.
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उत्तर
We have, 2n+2 + 2n+1 + 2n = c × 2n
⇒ 2n22 + 2n21 + 2n = c × 2n ...[∴ am+n = am × an]
⇒ 2n[22 – 21 + 1] = c × 2n ...[Taking common 2n in LHS]
⇒ 2n[4 – 2 + 1] = c × 2n
⇒ 3 × 2n = c × 2n
3 × 2n × 2–n = c × 3n × c–n ...[Multiplying both sides by 2–n]
⇒ 3 × 2n–1 = c × 2n–n ...[∴ am+n = am × an]
⇒ 3 × 20 = c × 20
⇒ 3 × 1 = c × 1 ...[∴ a0 = 1]
∴ 3 = c
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