Question

2^n-1+2^n+1=320 then n=?

Answer 1

ANS = 2^n-1+2^n+1=320

2 ^n)(2^-1 +2^+1 )= 320
 2^n ( 1/2 + 2) = 320
2 ^n( 5/2) = 320
2^n = 320*2/5
2^n=64*2
2^n=128
2^n=2^7
thus, n = 7 

Answer 2

Answer:

n = 7

Explanation:

Given

$2^{n-1}+2^{n+1}=320$

$\implies \frac{2^{n}}{2^{1}}+2^{n}\times 2^{1} = 320$

/* By Exponential laws :

i ) $a^{m-n} =\frac{a^{m}}{a^{n}}$

ii) $a^{m+n} = a^{m} \times a^{n}$

*/

Let 2ⁿ = a ---(1)

$\implies \frac{a}{2}+a \times 2 = 320$

$\implies \frac{a+4a}{2}=320$

$\implies \frac{5a}{2}=320$

$\implies a = 320 \times \frac{2}{5}$

After cancellation , we get

$\implies a = 128$

$\implies 2^{n} = 2^{7}$

/* From (1) */

$\implies n = 7$

/* By the Exponential Law :

$If \:a^{m}=a^{n} \: then \: m = n$ */

Therefore,

n = 7

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