Question

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

Answer 1

$\frac{ {4}^{n + 1} \times {2}^{n} - {8}^{n} }{ {2}^{3m} } = \frac{3}{8}$
$\frac{ {2}^{2n + 2} \times {2}^{n} - {2}^{3n} }{ {2}^{3m} } = \frac{3}{ {2}^{3} }$
$\frac{ {2}^{3n + 2} - {2}^{3n} }{ {2}^{3m} } = \frac{3}{ {2}^{3} }$
$\frac { {2}^{3n} ({2}^{ 2} - 1)}{ {2}^{3m} } = \frac{3}{ {2}^{3} }$
$\frac { {2}^{3n} \times 3}{ {2}^{3m} } = \frac{3}{ {2}^{3} }$
$\frac { {2}^{3n} }{ {2}^{3m} } = \frac{1}{ {2}^{3} }$
${2}^{3n - 3m} = {2}^{ - 3}$
$3n - 3m = - 3$
$n - m = - 1$
$n + 1 = m$
$proved.....$
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Answer 2

Answer:

the answer is -1

Step-by-step explanation:

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