\Rightarrow x\in(-\infty;\;-2)\cup(0;\;+\infty)\\-\log_3(x^2+2x)=-1\\\log_3(x^2+2x)=\log_33\\x^2+2x-3=0\\D=16\\x_1=-3,\;x_2=1\\b)\;\lg^2x+\lg x00\\O.D.3.:\;x>0\\\lg x=t,\;\lg^2x=t^2,\;\\t^2+t=0\\t(t+1)=0\\t_1=0\Rightarrow\lg x=10^0=1\Rightarrow x=1\\t_2=-1\Rightarrow\lg x=-1\Rightarrow x=10^{-1}=0,1" alt="1.a)\;\log_{\frac13}(x^2+2x)=-1\\O.D.3.:\;x^2+2x>\Rightarrow x\in(-\infty;\;-2)\cup(0;\;+\infty)\\-\log_3(x^2+2x)=-1\\\log_3(x^2+2x)=\log_33\\x^2+2x-3=0\\D=16\\x_1=-3,\;x_2=1\\b)\;\lg^2x+\lg x00\\O.D.3.:\;x>0\\\lg x=t,\;\lg^2x=t^2,\;\\t^2+t=0\\t(t+1)=0\\t_1=0\Rightarrow\lg x=10^0=1\Rightarrow x=1\\t_2=-1\Rightarrow\lg x=-1\Rightarrow x=10^{-1}=0,1" align="absmiddle" class="latex-formula">
-1\\-\log_4(2x-5)>-\log_44\\2x-5<4\\2x<9\\x<4,5\\\\3.\;y=e^x(3x-1)\\y'=e^x(3x-1)+3e^x=e^x(3x+2)\\e^x(3x+2)=0\\e^x\neq0\Rightarrow3x+2=0\Rightarrow x=-\frac23\\y\left(-\frac23\right)=e^{\frac23}(-2-1)=-3e^{\frac23}" alt="2.\;\log_{\frac14}(2x-5)>-1\\-\log_4(2x-5)>-\log_44\\2x-5<4\\2x<9\\x<4,5\\\\3.\;y=e^x(3x-1)\\y'=e^x(3x-1)+3e^x=e^x(3x+2)\\e^x(3x+2)=0\\e^x\neq0\Rightarrow3x+2=0\Rightarrow x=-\frac23\\y\left(-\frac23\right)=e^{\frac23}(-2-1)=-3e^{\frac23}" align="absmiddle" class="latex-formula">
- точка экстремума.
0\\y>0\end{cases}\\\begin{cases}\log_6(xy)=\log_66\\x+y=5\end{cases}\Rightarrow\begin{cases}xy=6\\x+y=5\end{cases}\Rightarrow\\\Rightarrow\begin{cases}x(5-x)=6\\y=5-x\end{cases}\\5x-x^2=6\\x^2-5x+6=0\\D=1\\x_1=2,\;x_2=3\\\begin{cases}x=2\\y=3\end{cases}\quad\quad\quad\begin{cases}x=3\\y=2\end{cases}" alt="4.\;\begin{cases}\log_6x+\log_6y=1\\x+y=5\end{cases}\\O.D.3.:\begin{cases}x>0\\y>0\end{cases}\\\begin{cases}\log_6(xy)=\log_66\\x+y=5\end{cases}\Rightarrow\begin{cases}xy=6\\x+y=5\end{cases}\Rightarrow\\\Rightarrow\begin{cases}x(5-x)=6\\y=5-x\end{cases}\\5x-x^2=6\\x^2-5x+6=0\\D=1\\x_1=2,\;x_2=3\\\begin{cases}x=2\\y=3\end{cases}\quad\quad\quad\begin{cases}x=3\\y=2\end{cases}" align="absmiddle" class="latex-formula">