ОДЗ :
0\\\\2^{x}<9\\\\x<log_{2}9\\\\log_{2} (9-2^{x})=3-x\\\\9-2^{x}=2^{3-x}\\\\9-2^{x}-8*2^{-x}=0\\\\2^{x}=m,m>0\\\\m+\frac{8}{m}-9=0\\\\m^{2}-9m+8=0\\\\m_{1}=8\\\\m_{2}=1\\\\2^{x}=8\\\\2^{x}=2^{3}\\\\x_{1}=3\\\\2^{x}=1\\\\2^{x}=2^{o}\\\\x_{2}=0" alt="9-2^{x}>0\\\\2^{x}<9\\\\x<log_{2}9\\\\log_{2} (9-2^{x})=3-x\\\\9-2^{x}=2^{3-x}\\\\9-2^{x}-8*2^{-x}=0\\\\2^{x}=m,m>0\\\\m+\frac{8}{m}-9=0\\\\m^{2}-9m+8=0\\\\m_{1}=8\\\\m_{2}=1\\\\2^{x}=8\\\\2^{x}=2^{3}\\\\x_{1}=3\\\\2^{x}=1\\\\2^{x}=2^{o}\\\\x_{2}=0" align="absmiddle" class="latex-formula">