If $2^{x - 1} + 2^{x + 1} = 320$ , then x equals

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Solution

The correct option is D 7
$2^{x - 1} + 2^{x + 1} = 320$
if x=4 then
$2^{4 - 1} + 2^{4 + 1} = 320$
$2^{3} + 2^{5} = 320$
$40 \neq 320$
if x=5 then
$2^{5 - 1} + 2^{5 + 1} = 320$
$2^{4} + 2^{6} = 320$
$80 \neq 320$
if x=6 then
$2^{6 - 1} + 2^{6 + 1} = 320$
$2^{5} + 2^{7} = 320$
$160 \neq 320$
if x=7 then
$2^{7 - 1} + 2^{7 + 1} = 320$
$2^{6} + 2^{8} = 320$
$320 = 320$
Hence x=7

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