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If m and n are natural numbers such that \( \Large 2^{m}-2^{n}=960 \), then what is the value of m?

A) 10
B) 12
C) 16
D) Cannot be determined

Correct Answer:

A) 10

Description for Correct answer:
Given: \( \Large 2^{m}-2^{n}=960 \)

=> \( \Large 2^{n} \left(2^{m-n}-1\right)=960 \)

=> \( \Large 2^{n} \left(2^{m-n}-1\right)=64 \times \left(16-1\right) \)

=> \( \Large 2^{n} \left(2^{m-n}-1\right)=2^{6} \times \left(2^{4}-1\right) \)

Equating, we have

\( \Large n = 6 \)

and \( \Large m-n = 4 \)

=> \( \Large m-6 = 4 \)

=> \( \Large m = 10 \)

Part of solved Polynomials questions and answers : >> Elementary Mathematics >> Polynomials

Comments

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