Question

Помогите пожалуйста решить 4 и 5 задания

Answer 1

$log_{x+1}(x+3) textless 1, \ left{begin{array}{c}x+3 textgreater 0,\ left[begin{array}{c}left { {{0 textless x+1 textless 1,} atop {x+3 textgreater x+1,}} right.\ left { {{x+1 textgreater 1,} atop {x+3 textless x+1,}} right.end{array}right. end{array}right. left{begin{array}{c}x textgreater -3,\ left[begin{array}{c}left { {{-1 textless x textless 0,} atop {0cdot x textgreater -2,}} right.\ left { {{x textgreater 0,} atop {0cdot x textless -2,}} right.end{array}right. end{array}right.$
$left{begin{array}{c}x textgreater -3,\ left[begin{array}{c}left { {{-1 textless x textless 0,} atop {xin R,}} right.\ left { {{x textgreater 0,} atop {xinvarnothing,}} right.end{array}right. end{array}right. left{begin{array}{c}x textgreater -3,\ left[begin{array}{c} -1 textless x textless 0, \ xinvarnothing, end{array}right. end{array}right. left { {{x textgreater -3} atop {-1 textless x textless 0,}} right. \ -1 textless x textless 0, \ xin(-1;0)$

$|2+frac{x}{9}|^{log_3|2+frac{x}{9}|}=81, \ |2+frac{x}{9}| textgreater 0, 2+frac{x}{9}neq0, x neq -18; \ |2+frac{x}{9}|=a, \ a^{log_3a}=81, \ log_3a^{log_3a}=log_33^4, \ log_3alog_3a=4, \ log_3^2a=4, \ left [ {{log_3a=-2,} atop {log_3a=2;}} right. left [ {{a=frac{1}{9},} atop {a=9;}} right. left [ {{|2+frac{x}{9}|=frac{1}{9},} atop {|2+frac{x}{9}|=9;}} right.$
$left[begin{array}{c} 2+frac{x}{9}=-frac{1}{9}, \ 2+frac{x}{9}=frac{1}{9}, \ 2+frac{x}{9}=-9, \ 2+frac{x}{9}=9, end{array}right. left[begin{array}{c} x=-19, \ x=-17, \ x=99, \ x=63. end{array}right.$

Answer 2

В самой нижней совокупности уравнений опечатка. Корень должен быть x=-99, а не x=99.