Question

Решите пожалуйста неравенства:

Answer 1

(1)
$log_3^2(4-x) textless 1\\ log_3^2(4-x)-1^2 textless 0\\ (log_3(4-x)+1)*(log_3(4-x)-1) textless 0\\ -1 textless log_3(4-x) textless 1\\ begin{equation*} begin{cases} log_3(4-x) textgreater -1\ log_3(4-x) textless 1 end{cases} end{equation*}\\ begin{equation*} begin{cases} log_3(4-x) textgreater log_3(3^{-1})\ log_3(4-x) textless log_3(3) end{cases} end{equation*} begin{equation*} begin{cases} 4-x textgreater frac{1}{3}\ 4-x textless 3\ 4-x textgreater 0 end{cases} end{equation*}$

$begin{equation*} begin{cases} x textless frac{11}{3}\ x textgreater 1\ x textless 4 end{cases} end{equation*}$

$xin(1; frac{11}{3})$
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(2)
$log_{0.2}^2(x)-5*log_{0.2}(x) textless -6\\ log_{0.2}^2(x)-5*log_{0.2}(x)+6 textless 0\\ (log_{0.2}(x)-2)*(log_{0.2}(x)-3) textless 0\\ 2 textless log_{0.2}(x) textless 3\\ 2 textless log_{5^{-1}}(x) textless 3\\ 2 textless -log_{5}}(x) textless 3\\ left { {{log_{5}}(x) textless -2} atop {log_{5}}(x) textgreater -3}} right. ;\\ left { {{log_{5}}(x) textless log_5(5^{-2})} atop {log_{5}}(x) textgreater log_5(5^{-3})}} right. \\ left { {{x textless frac{1}{25}} atop {x textgreater frac{1}{125}}}\ atop {x textgreater 0} right. \\ xin(frac{1}{125}}; frac{1}{25}})$

Answer 2

а) ОТВЕТ: $mathtt{xin(1;frac{11}{3})}$

$mathtt{log_3^2(4-x)-1 textless 0;~(log_3(4-x)-1)(log_3(4-x)+1) textless 0;~}\mathtt{-1 textless log_3(4-x) textless 1;~frac{1}{3} textless 4-x textless 3;~-3 textless x-4 textless -frac{1}{3};~1 textless x textless frac{11}{3}}$

б) ОТВЕТ: $mathtt{xin(frac{1}{125};frac{1}{25})}$

$mathtt{log_{0,2}^2x-5log_{0,2}x textless -6;~log_5^2x+5log_5x+6 textless 0;~}\mathtt{(log_5x+3)(log_5x+2) textless 0;~-3 textless log_5x textless -2;~frac{1}{5^3} textless x textless frac{1}{5^2}}$