Question

answer this question as fast as possible​

Answer 1

Given,

$\longrightarrow\sf{2^{n-1}+2^{n+1}=320}$

We can take $\sf{2^{n-1}}$ as common in LHS as follows:

$\longrightarrow\sf{2^{n-1}+2^{n-1+2}=320}$

$\longrightarrow\sf{2^{n-1}+2^{n-1}\times2^2=320}$

$\longrightarrow\sf{2^{n-1}\left[1+2^2\right]=320}$

$\longrightarrow\sf{2^{n-1}\left[1+4\right]=320}$

$\longrightarrow\sf{2^{n-1}\times5=320}$

$\longrightarrow\sf{2^{n-1}=\dfrac{320}{5}}$

$\longrightarrow\sf{2^{n-1}=64}$

Then,

$\longrightarrow\sf{n-1=\log_264}$

$\longrightarrow\sf{n-1=6}$

$\longrightarrow\sf{\underline{\underline{n=7}}}$

Hence 7 is the answer.