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(1)
![log_3^2(4-x) textless 1\\
log_3^2(4-x)-1^2 textless 0\\
(log_3(4-x)+1)*(log_3(4-x)-1) textless 0\\
-1 textless log_3(4-x) textless 1\\
begin{equation*}
begin{cases}
log_3(4-x) textgreater -1\
log_3(4-x) textless 1
end{cases}
end{equation*}\\
begin{equation*}
begin{cases}
log_3(4-x) textgreater log_3(3^{-1})\
log_3(4-x) textless log_3(3)
end{cases}
end{equation*}
begin{equation*}
begin{cases}
4-x textgreater frac{1}{3}\
4-x textless 3\
4-x textgreater 0
end{cases}
end{equation*}
log_3^2(4-x) textless 1\\
log_3^2(4-x)-1^2 textless 0\\
(log_3(4-x)+1)*(log_3(4-x)-1) textless 0\\
-1 textless log_3(4-x) textless 1\\
begin{equation*}
begin{cases}
log_3(4-x) textgreater -1\
log_3(4-x) textless 1
end{cases}
end{equation*}\\
begin{equation*}
begin{cases}
log_3(4-x) textgreater log_3(3^{-1})\
log_3(4-x) textless log_3(3)
end{cases}
end{equation*}
begin{equation*}
begin{cases}
4-x textgreater frac{1}{3}\
4-x textless 3\
4-x textgreater 0
end{cases}
end{equation*}](https://tex.z-dn.net/?f=log_3%5E2%284-x%29+textless++1%5C%5C%0Alog_3%5E2%284-x%29-1%5E2+textless++0%5C%5C%0A%28log_3%284-x%29%2B1%29%2A%28log_3%284-x%29-1%29+textless++0%5C%5C%0A-1+textless++log_3%284-x%29+textless++1%5C%5C%0Abegin%7Bequation%2A%7D%0A%09begin%7Bcases%7D%0A%09%09log_3%284-x%29+textgreater++-1%5C%0A%09%09log_3%284-x%29+textless++1%0A%09end%7Bcases%7D%0Aend%7Bequation%2A%7D%5C%5C%0Abegin%7Bequation%2A%7D%0A%09begin%7Bcases%7D%0A%09%09log_3%284-x%29+textgreater++log_3%283%5E%7B-1%7D%29%5C%0A%09%09log_3%284-x%29+textless++log_3%283%29%0A%09end%7Bcases%7D%0Aend%7Bequation%2A%7D%0Abegin%7Bequation%2A%7D%0A%09begin%7Bcases%7D%0A%09%094-x+textgreater++frac%7B1%7D%7B3%7D%5C%0A%09%094-x+textless++3%5C%0A++++++++++++++++4-x+textgreater++0%0A%09end%7Bcases%7D%0Aend%7Bequation%2A%7D%0A)
![begin{equation*}
begin{cases}
x textless frac{11}{3}\
x textgreater 1\
x textless 4
end{cases}
end{equation*} begin{equation*}
begin{cases}
x textless frac{11}{3}\
x textgreater 1\
x textless 4
end{cases}
end{equation*}](https://tex.z-dn.net/?f=begin%7Bequation%2A%7D%0A%09begin%7Bcases%7D%0A%09%09x+textless++frac%7B11%7D%7B3%7D%5C%0A%09%09x+textgreater++1%5C%0A++++++++++++++++x+textless++4%0A%09end%7Bcases%7D%0Aend%7Bequation%2A%7D)
![xin(1; frac{11}{3}) xin(1; frac{11}{3})](https://tex.z-dn.net/?f=xin%281%3B+frac%7B11%7D%7B3%7D%29)
---------------------------------------
(2)
![log_{0.2}^2(x)-5*log_{0.2}(x) textless -6\\
log_{0.2}^2(x)-5*log_{0.2}(x)+6 textless 0\\
(log_{0.2}(x)-2)*(log_{0.2}(x)-3) textless 0\\
2 textless log_{0.2}(x) textless 3\\
2 textless log_{5^{-1}}(x) textless 3\\
2 textless -log_{5}}(x) textless 3\\
left { {{log_{5}}(x) textless -2} atop {log_{5}}(x) textgreater -3}} right. ;\\
left { {{log_{5}}(x) textless log_5(5^{-2})} atop {log_{5}}(x) textgreater log_5(5^{-3})}} right. \\
left { {{x textless frac{1}{25}} atop {x textgreater frac{1}{125}}}\ atop {x textgreater 0} right. \\
xin(frac{1}{125}}; frac{1}{25}}) log_{0.2}^2(x)-5*log_{0.2}(x) textless -6\\
log_{0.2}^2(x)-5*log_{0.2}(x)+6 textless 0\\
(log_{0.2}(x)-2)*(log_{0.2}(x)-3) textless 0\\
2 textless log_{0.2}(x) textless 3\\
2 textless log_{5^{-1}}(x) textless 3\\
2 textless -log_{5}}(x) textless 3\\
left { {{log_{5}}(x) textless -2} atop {log_{5}}(x) textgreater -3}} right. ;\\
left { {{log_{5}}(x) textless log_5(5^{-2})} atop {log_{5}}(x) textgreater log_5(5^{-3})}} right. \\
left { {{x textless frac{1}{25}} atop {x textgreater frac{1}{125}}}\ atop {x textgreater 0} right. \\
xin(frac{1}{125}}; frac{1}{25}})](https://tex.z-dn.net/?f=log_%7B0.2%7D%5E2%28x%29-5%2Alog_%7B0.2%7D%28x%29+textless++-6%5C%5C%0Alog_%7B0.2%7D%5E2%28x%29-5%2Alog_%7B0.2%7D%28x%29%2B6+textless++0%5C%5C%0A%28log_%7B0.2%7D%28x%29-2%29%2A%28log_%7B0.2%7D%28x%29-3%29+textless++0%5C%5C%0A2+textless++log_%7B0.2%7D%28x%29+textless++3%5C%5C%0A2+textless++log_%7B5%5E%7B-1%7D%7D%28x%29+textless++3%5C%5C%0A2+textless++-log_%7B5%7D%7D%28x%29+textless++3%5C%5C%0A+left+%7B+%7B%7Blog_%7B5%7D%7D%28x%29+textless++-2%7D+atop+%7Blog_%7B5%7D%7D%28x%29+textgreater++-3%7D%7D+right.+%3B%5C%5C%0A+left+%7B+%7B%7Blog_%7B5%7D%7D%28x%29+textless++log_5%285%5E%7B-2%7D%29%7D+atop+%7Blog_%7B5%7D%7D%28x%29+textgreater++log_5%285%5E%7B-3%7D%29%7D%7D+right.+%5C%5C%0A+left+%7B+%7B%7Bx+textless++frac%7B1%7D%7B25%7D%7D+atop+%7Bx+textgreater++frac%7B1%7D%7B125%7D%7D%7D%5C+atop+%7Bx+textgreater++0%7D+right.+%5C%5C%0Axin%28frac%7B1%7D%7B125%7D%7D%3B+frac%7B1%7D%7B25%7D%7D%29)
---------------------------------------
(2)
Ответ дал:
0
а) ОТВЕТ: ![mathtt{xin(1;frac{11}{3})} mathtt{xin(1;frac{11}{3})}](https://tex.z-dn.net/?f=mathtt%7Bxin%281%3Bfrac%7B11%7D%7B3%7D%29%7D)
![mathtt{log_3^2(4-x)-1 textless 0;~(log_3(4-x)-1)(log_3(4-x)+1) textless 0;~}\mathtt{-1 textless log_3(4-x) textless 1;~frac{1}{3} textless 4-x textless 3;~-3 textless x-4 textless -frac{1}{3};~1 textless x textless frac{11}{3}} mathtt{log_3^2(4-x)-1 textless 0;~(log_3(4-x)-1)(log_3(4-x)+1) textless 0;~}\mathtt{-1 textless log_3(4-x) textless 1;~frac{1}{3} textless 4-x textless 3;~-3 textless x-4 textless -frac{1}{3};~1 textless x textless frac{11}{3}}](https://tex.z-dn.net/?f=mathtt%7Blog_3%5E2%284-x%29-1+textless++0%3B%7E%28log_3%284-x%29-1%29%28log_3%284-x%29%2B1%29+textless++0%3B%7E%7D%5Cmathtt%7B-1+textless++log_3%284-x%29+textless++1%3B%7Efrac%7B1%7D%7B3%7D+textless++4-x+textless++3%3B%7E-3+textless++x-4+textless++-frac%7B1%7D%7B3%7D%3B%7E1+textless++x+textless++frac%7B11%7D%7B3%7D%7D)
б) ОТВЕТ:![mathtt{xin(frac{1}{125};frac{1}{25})} mathtt{xin(frac{1}{125};frac{1}{25})}](https://tex.z-dn.net/?f=mathtt%7Bxin%28frac%7B1%7D%7B125%7D%3Bfrac%7B1%7D%7B25%7D%29%7D)
![mathtt{log_{0,2}^2x-5log_{0,2}x textless -6;~log_5^2x+5log_5x+6 textless 0;~}\mathtt{(log_5x+3)(log_5x+2) textless 0;~-3 textless log_5x textless -2;~frac{1}{5^3} textless x textless frac{1}{5^2}} mathtt{log_{0,2}^2x-5log_{0,2}x textless -6;~log_5^2x+5log_5x+6 textless 0;~}\mathtt{(log_5x+3)(log_5x+2) textless 0;~-3 textless log_5x textless -2;~frac{1}{5^3} textless x textless frac{1}{5^2}}](https://tex.z-dn.net/?f=mathtt%7Blog_%7B0%2C2%7D%5E2x-5log_%7B0%2C2%7Dx+textless++-6%3B%7Elog_5%5E2x%2B5log_5x%2B6+textless++0%3B%7E%7D%5Cmathtt%7B%28log_5x%2B3%29%28log_5x%2B2%29+textless++0%3B%7E-3+textless++log_5x+textless++-2%3B%7Efrac%7B1%7D%7B5%5E3%7D+textless++x+textless++frac%7B1%7D%7B5%5E2%7D%7D)
б) ОТВЕТ:
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