![image](https://tex.z-dn.net/?f=%0A+2%5Ex%2B2%5Ey%3D%5Cfrac%7B1%7D%7B128%7D%5C%5C%0A+log_%7B3%7Dx%2Blog_%7B3%7Dy%3D2%2Blog_%7B3%7D2%5C%5C%5C%5C+%0A2%5Ex%2B2%5Ey%3D%5Cfrac%7B1%7D%7B2%5E7%7D%5C%5C%0Alog_%7B3%7D%28xy%29%3Dlog_%7B3%7D9%2Blog_%7B3%7D2%5C%5C%5C%5C%0A+2%5Ex%2B2%5Ey%3D%5Cfrac%7B1%7D%7B2%5E7%7D%5C%5C%0A+log_%7B3%7D%28xy%29%3Dlog_%7B3%7D18+%5C%5C%5C%5C+%0A+xy%3D18%5C%5C%0A+x%3D%5Cfrac%7B18%7D%7By%7D%5C%5C%0A++x%3By%3E0%5C%5C%5C%5C%0A+2%5E%7B%5Cfrac%7B18%7D%7By%7D%7D%2B2%5Ey%3D%5Cfrac%7B1%7D%7B128%7D%5C%5C%5C%5C%0A%0A)
0\\\\
2^{\frac{18}{y}}+2^y=\frac{1}{128}\\\\
" alt="
2^x+2^y=\frac{1}{128}\\
log_{3}x+log_{3}y=2+log_{3}2\\\\
2^x+2^y=\frac{1}{2^7}\\
log_{3}(xy)=log_{3}9+log_{3}2\\\\
2^x+2^y=\frac{1}{2^7}\\
log_{3}(xy)=log_{3}18 \\\\
xy=18\\
x=\frac{18}{y}\\
x;y>0\\\\
2^{\frac{18}{y}}+2^y=\frac{1}{128}\\\\
" align="absmiddle" class="latex-formula">
видно что решений нет так как
![image](https://tex.z-dn.net/?f=+2%5E%7B%5Cfrac%7B18%7D%7By%7D%2B7%7D%2B2%5E%7By%2B7%7D%3D1%5C%5C%0Ay%3E0)
0" alt=" 2^{\frac{18}{y}+7}+2^{y+7}=1\\
y>0" align="absmiddle" class="latex-formula">