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If $2^{n-1}+2^{n+1}=320$ then n is equal to:

Answer:

Explanation:

$2^{n-1}+2^{n+1}=320$ $\Leftrightarrow 2^{n-1} \left( 1+ 2^{2}\right)=320$ $\Leftrightarrow 5 \times 2^{n-1} = 320$ $\Leftrightarrow 2^{n-1} = \frac{320}{5}$ $=64=2^{6}$ $\Leftrightarrow n-1=6$ $\Leftrightarrow n=7$