Question

Помогите, пожалуйста, с логарифмическими неравенствами - 3 штуки) Буду вам очень благодарна, нужны все 3))

Answer 1

1) $log_{0,7}(3-2x)-log_{0,7}54 textgreater log_{0,7}frac{1}{2}-log_{0,7}9;\ begin{cases}log_{0,7}(3-2x) textgreater log_{0,7}54+log_{0,7}frac{1}{2}-log_{0,7}9,\3-2x textgreater 0;end{cases}\ begin{cases}log_{0,7}(3-2x) textgreater log_{0,7}(54cdotfrac{1}{2}:9),\2x textless 3;end{cases};\ begin{cases}3-2x textless 3,\x textless 1,5;end{cases},begin{cases}x textgreater 0,\x textless 1,5;end{cases},xin(0;1,5)$
2) $log_2log_{sqrt{5}}(x-1) textless 1;\ begin{cases}log_2log_{sqrt{5}}(x-1) textless log_22,\ log_{sqrt{5}}(x-1) textgreater 0,\ x-1 textgreater 0;end{cases},begin{cases}log_{sqrt{5}}(x-1) textless 2,\ log_{sqrt{5}}(x-1) textgreater log_{sqrt{5}}1,\ x textgreater 1;end{cases}\ begin{cases}log_{sqrt{5}}(x-1) textless log_{sqrt{5}}5,\ x-1 textgreater 1,\ x textgreater 1;end{cases}, begin{cases}x-1 textless 5,\ x textgreater 2;end{cases},begin{cases}x textless 6,\ x textgreater 2;end{cases},xin(2;6)$
3)  $log_{frac{1}{3}}(x+2)-log_{3}(x+2) textgreater -frac{3}{2};\ begin{cases}-log_{3}(x+2)-log_{3}(x+2) textgreater -frac{3}{2},\x+2 textgreater 0;end{cases}\ begin{cases}2log_{3}(x+2) textless frac{3}{2},\x textgreater -2;end{cases},begin{cases}log_{3}(x+2) textless frac{3}{4},\x textgreater -2;end{cases},begin{cases}x+2 textless sqrt[4]{27},\x textgreater -2;end{cases}\ begin{cases}x textless sqrt[4]{27}-2,\x textgreater -2;end{cases},xin(-2;sqrt[4]{27}-2)$