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Question: If \(\frac{(2^{n + 1})^{m}(2^{2n})2^{n}}{(2^{m + 1})^{n}2^{2m}} = 1,\) then m =...

If (2n+1)m(22n)2n(2m+1)n22m=1,\frac{(2^{n + 1})^{m}(2^{2n})2^{n}}{(2^{m + 1})^{n}2^{2m}} = 1, then m =

A

0

B

1

C

n

D

2n

Answer

2n

Explanation

Solution

2m(n+1)+2n+n=2(m+1)n+2m2^{m(n + 1) + 2n + n} = 2^{(m + 1)n + 2m}

⇒mn+m+3n=mn+2m+n⇒m=2n\Rightarrow mn + m + 3n = mn + 2m + n \Rightarrow m = 2n.