![1)\;\log_{\frac12}\sqrt[3]{2x-2}=-2\\\log_{2^{-1}}(2x-2)^{\frac13}=-2\\-\frac13\log_2(2x-2)=-2\\\log_2(2x-2)=6\\2x-2=2^6\\2x-2=64\\2x=66\\x=33](https://tex.z-dn.net/?f=1%29%5C%3B%5Clog_%7B%5Cfrac12%7D%5Csqrt%5B3%5D%7B2x-2%7D%3D-2%5C%5C%5Clog_%7B2%5E%7B-1%7D%7D%282x-2%29%5E%7B%5Cfrac13%7D%3D-2%5C%5C-%5Cfrac13%5Clog_2%282x-2%29%3D-2%5C%5C%5Clog_2%282x-2%29%3D6%5C%5C2x-2%3D2%5E6%5C%5C2x-2%3D64%5C%5C2x%3D66%5C%5Cx%3D33 "1)\;\log_{\frac12}\sqrt[3]{2x-2}=-2\\\log_{2^{-1}}(2x-2)^{\frac13}=-2\\-\frac13\log_2(2x-2)=-2\\\log_2(2x-2)=6\\2x-2=2^6\\2x-2=64\\2x=66\\x=33")
0\Rightarrow x\in\left(-\frac{3+\sqrt{13}}2;\;-\frac{3-\sqrt{13}}{2}\right)\approx(-3,3;\;0,3)\\\\\begin{cases}x^2-4=0\\\log_3(1-x^2-3x)=0\end{cases}\Rightarrow\begin{cases}x_1=-2\\x_2=2\\1-x^2-3x=1\end{cases}\Rightarrow\\\Rightarrow\begin{cases}x_1=-2\\x_2=2\;He\;nogx.\\x(x+3)=0\end{cases}\Rightarrow\begin{cases}x_1=-2\\x_2=2\\x_3=0\\x_4=-3\end{cases}" alt="2)\;(x^2-4)\log_3(1-x^2-3x)=0\\O.D.3.:\\1-x^2-3x>0\Rightarrow x\in\left(-\frac{3+\sqrt{13}}2;\;-\frac{3-\sqrt{13}}{2}\right)\approx(-3,3;\;0,3)\\\\\begin{cases}x^2-4=0\\\log_3(1-x^2-3x)=0\end{cases}\Rightarrow\begin{cases}x_1=-2\\x_2=2\\1-x^2-3x=1\end{cases}\Rightarrow\\\Rightarrow\begin{cases}x_1=-2\\x_2=2\;He\;nogx.\\x(x+3)=0\end{cases}\Rightarrow\begin{cases}x_1=-2\\x_2=2\\x_3=0\\x_4=-3\end{cases}" align="absmiddle" class="latex-formula">
0\\1-\lg x\neq0\end{cases}\Rightarrow\begin{cases}x>0\\x\neq10\end{cases}\Rightarrow x\in(0;\
;10)\cup(10;\;+\infty)\\\\\lg x=3-3\lg x\\4\lg x=3\\\lg x=\frac34\\x=10^{\frac34}=\sqrt[4]{1000}" alt="3)\;\frac{\lg x}{1-\lg x}=3\\O.D.3.:\\\begin{cases}x>0\\1-\lg x\neq0\end{cases}\Rightarrow\begin{cases}x>0\\x\neq10\end{cases}\Rightarrow x\in(0;\
;10)\cup(10;\;+\infty)\\\\\lg x=3-3\lg x\\4\lg x=3\\\lg x=\frac34\\x=10^{\frac34}=\sqrt[4]{1000}" align="absmiddle" class="latex-formula">