![image](https://tex.z-dn.net/?f=%5Clog_2%286-x%29%2B%5Clog_2x%3D3%5C%5CO.D.3.%3A%5C%5C%5Cbegin%7Bcases%7D6-x%3E0%5C%5Cx%3E0%5Cend%7Bcases%7D%5CRightarrow%5Cbegin%7Bcases%7Dx%3C6%5C%5Cx%3E0%5Cend%7Bcases%7D%5CRightarrow+x%5Cin%280%3B%5C%3B6%29%5C%5C%5Clog_2%28x%286-x%29%29%3D%5Clog_28%5C%5C6x-x%5E2%3D8%5C%5Cx%5E2-6x%2B8%3D0%5C%5CD%3D36-4%5Ccdot8%3D4%5C%5Cx_1%3D2%2C%5C%3Bx_2%3D4)
0\\x>0\end{cases}\Rightarrow\begin{cases}x<6\\x>0\end{cases}\Rightarrow x\in(0;\;6)\\\log_2(x(6-x))=\log_28\\6x-x^2=8\\x^2-6x+8=0\\D=36-4\cdot8=4\\x_1=2,\;x_2=4" alt="\log_2(6-x)+\log_2x=3\\O.D.3.:\\\begin{cases}6-x>0\\x>0\end{cases}\Rightarrow\begin{cases}x<6\\x>0\end{cases}\Rightarrow x\in(0;\;6)\\\log_2(x(6-x))=\log_28\\6x-x^2=8\\x^2-6x+8=0\\D=36-4\cdot8=4\\x_1=2,\;x_2=4" align="absmiddle" class="latex-formula">