\log_{0.2}(2x-3)\\
\left\lbrace\begin{array}{l}
\log_{0.2}x(x-2)>\log_{0.2}(2x-3)\\
x>2
\end{array}\right.\\
\left\lbrace\begin{array}{l}
x^2-2x<2x-3\\
x>2
\end{array}\right.\\
\left\lbrace\begin{array}{l}
x^2-4x+3<0\\
x>2
\end{array}\right.\\
\boxed{x\in(2,3)}" alt="\log_{0.2}(x-2)+\log_{0.2}x>\log_{0.2}(2x-3)\\
\left\lbrace\begin{array}{l}
\log_{0.2}x(x-2)>\log_{0.2}(2x-3)\\
x>2
\end{array}\right.\\
\left\lbrace\begin{array}{l}
x^2-2x<2x-3\\
x>2
\end{array}\right.\\
\left\lbrace\begin{array}{l}
x^2-4x+3<0\\
x>2
\end{array}\right.\\
\boxed{x\in(2,3)}" align="absmiddle" class="latex-formula">
![\dfrac{\sqrt{36-x^2}\cdot\log_{0.5}x}{x-2}\leqslant0\\ \left\lbrace\begin{array}{l} \left[\begin{array}{l} x^2=36\\ \dfrac{x-1}{x-2}\geqslant0 \end{array}\right.\\ x\in(0,2)\cup(2,6]\\ \end{array}](https://tex.z-dn.net/?f=%5Cdfrac%7B%5Csqrt%7B36-x%5E2%7D%5Ccdot%5Clog_%7B0.5%7Dx%7D%7Bx-2%7D%5Cleqslant0%5C%5C+%5Cleft%5Clbrace%5Cbegin%7Barray%7D%7Bl%7D+%5Cleft%5B%5Cbegin%7Barray%7D%7Bl%7D+x%5E2%3D36%5C%5C+%5Cdfrac%7Bx-1%7D%7Bx-2%7D%5Cgeqslant0+%5Cend%7Barray%7D%5Cright.%5C%5C+x%5Cin%280%2C2%29%5Ccup%282%2C6%5D%5C%5C+%5Cend%7Barray%7D+ "\dfrac{\sqrt{36-x^2}\cdot\log_{0.5}x}{x-2}\leqslant0\\ \left\lbrace\begin{array}{l} \left[\begin{array}{l} x^2=36\\ \dfrac{x-1}{x-2}\geqslant0 \end{array}\right.\\ x\in(0,2)\cup(2,6]\\ \end{array}")
![\boxed{x\in(0,1]\cup(2,6]}](https://tex.z-dn.net/?f=%5Cboxed%7Bx%5Cin%280%2C1%5D%5Ccup%282%2C6%5D%7D "\boxed{x\in(0,1]\cup(2,6]}")
0\\
y^2+2x=29
\end{array}\right.\\
\left\lbrace\begin{array}{l}
x^2-x-2=0\\
y^2=29-2x\\
x+y+1>0
\end{array}\right.\\
\left\lbrace\begin{array}{l}
\left[\begin{array}{l}
x=2\\
x=-1
\end{array}\right.\\
y^2=29-2x\\
x+y+1>0
\end{array}\right.
" alt="\left\lbrace\begin{array}{l}
2^{\log_2(x+y+1)}=x^2+y-1\\
\log_{\sqrt{29}}(y^2+2x)=2
\end{array}\right.\\
\left\lbrace\begin{array}{l}
x+y+1=x^2+y-1\\
x+y+1>0\\
y^2+2x=29
\end{array}\right.\\
\left\lbrace\begin{array}{l}
x^2-x-2=0\\
y^2=29-2x\\
x+y+1>0
\end{array}\right.\\
\left\lbrace\begin{array}{l}
\left[\begin{array}{l}
x=2\\
x=-1
\end{array}\right.\\
y^2=29-2x\\
x+y+1>0
\end{array}\right.
" align="absmiddle" class="latex-formula">
0
\end{array}\right.\\
\boxed{(x,y)\in\lbrace(2,5),(-1,\sqrt{31})\rbrace}" alt="\left\lbrace\begin{array}{l}
\left[\begin{array}{l}
x=2, y^2=25\\
x=-1, y^2=31
\end{array}\right.\\
x+y+1>0
\end{array}\right.\\
\boxed{(x,y)\in\lbrace(2,5),(-1,\sqrt{31})\rbrace}" align="absmiddle" class="latex-formula">
