Question

If $2^{x-1} + 2^{x+1} = 320$, find the value of x.

Answer 1

(2^x)/2 +(2^x)*2=320
(2^x)+2^(x+2)=640
2.^x[1+4]=640
2.^x=128
x=7

Answer 2

Given Equation is 2^x-1 + 2^x+1 = 320.

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

$2^{x-1} + 2^{2} * 2^{x-1} = 320$

$2^{x-1} (1 + 2^{2})$ = 320

$5 * ( 2^{x-1} )$ = 320

$2^{x-1} = \frac{320}{5}$

$2^{x-1} = 64$

$2^{x-1} = 2^{6}$

x-1 = 6

x = 7.


Hope this helps!