Question

for some integers m and n 2^m-2^n =1792​

Answer 1

Answer:

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Step-by-step explanation:

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Answer 2

The values are m = 11 and n=8.

Given:

$2^{m} -2^{n} = 1792$

To Find:

The values of n and m.

Solution:

$2^{m} -2^{n} = 1792$

Taking $2^{n}$ outside in LHS

$2^{n}( \frac{2^{m}}{2^{n}} -1) = 1792\\\\2^{n}(2^{m-n} - 1 ) = 1792 \ \ ( \because \frac{a^{m} }{a^{n}} = a^{m-n} } )$

1792 = $2^{8} \times 7$

$2^{n}( 2^{m-n} -1) =2^{8} \times 7$

On comparing both sides

$2^{n} = 2^{8} \\\\\implies n = 8$ and

$2^{m-8} -1 = 7\\\\2^{m-8} = 8\\\\2^{m} = 8 \times 2^{8} \\\\2^{m} = 2^{11} \\\\\implies m = 11$

Therefore, The values are m = 11 and n=8.

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