Решите уравнение 2^x+2^x-2 +2^x-3=11\4

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 

[latex] 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[/latex]