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If (4^(n+1)×2^n-8^n)/2^3m =3/8,Prove that n+1=m

Answer»
\frac{ {4}^{n + 1} \times {2}^{n} - {8}^{n} }{ {2}^{3m} } = \frac{3}{8}
\frac{ {2}^{2n + 2} \times {2}^{n} - {2}^{3n} }{ {2}^{3m} } = \frac{3}{ {2}^{3} }
\frac{ {2}^{3n + 2} - {2}^{3n} }{ {2}^{3m} } = \frac{3}{ {2}^{3} }
\frac { {2}^{3n} ({2}^{ 2} - 1)}{ {2}^{3m} } = \frac{3}{ {2}^{3} }
\frac { {2}^{3n} \times 3}{ {2}^{3m} } = \frac{3}{ {2}^{3} }
\frac { {2}^{3n} }{ {2}^{3m} } = \frac{1}{ {2}^{3} }
{2}^{3n - 3m} = {2}^{ - 3}
3n - 3m = - 3
n - m = - 1
n + 1 = m
proved.....
I HOPE it's REALLY HELPFUL for you


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