Question

решите уравнение
2^x+2^x-2 +2^x-3=114

Answer 1

2 ^ X * ( 1 + ( 2 ^ - 2 ) + ( 2 ^ - 3 ) ) = 11/4 
2 ^ X * ( 1 + ( 1/4 ) + ( 1/8 ) = 11/4 
2 ^ X * ( ( 8/8 ) + ( 2/8 ) + ( 1/8 ) = 11/4 
2 ^ X * ( 11/8 ) = 11/4 
2 ^ X = ( 11/4 ) : ( 11/8 )
2 ^ X = 2 
X = 1 

Answer 2

$2^{x}+ 2^{x-2}+ 2^{x-3}= frac{11}{4} \ 1*2^{x}+2^{-2}*2^{x}+2^{-3}* 2^{x}= frac{11}{4} \ 2^{x}*(1+ frac{1}{4}+ frac{1}{8} )= frac{11}{4} \ 2^{x}*( frac{8}{8} + frac{2}{8}+ frac{1}{8} )= frac{11}{4} \ 2^{x}* frac{11}{8}= frac{11}{4} \ 2^{x}= frac{11}{4}:frac{11}{8} \ 2^{x}= frac{11}{4}*frac{8}{11} \ 2^{x}= 2 \ 2^{x}= 2^1 \ x=1$