5. Решите неравенство log2 (х- 2)^3 равно или меньше log4(х- 7)^6-12

{x-2>0⇒x>3 {x-7≠0⇒x≠7 x∈(3;7) U (7;∞) log(2)(x-2)³≤log(2)(x-7)³-12 3log(2)(x-3)≤3log(2)(x-7)-12 log(2)(x-3)≤log(2)(x-7)-4 log(2)(x-3)+4≤log(2)(x-7) log(2)(16x-48)≤log(2)(x-7) 16x-48≤x-7 15x≤41 x≤2 11/15 нет решения

x-2>0, x>2, x-7≠0, x≠7; x∈(2; 7)∪(7;+∞) [latex] log_{2}(x-2)^3 \ \leq log_{4}(x-7)^6-12 [/latex] [latex] 3log_{2}(x-2) \leq 3 log_{2}(x-7)-12 [/latex] [latex] log_{2} \frac{x-2}{x-7} \leq -4 [/latex] [latex] \frac{x-2}{x-7} \leq 2^{-4} [/latex] [latex] \frac{x-2}{x-7} \leq \frac{1}{16} [/latex] 16(x-2)≤x-7 16x-32≤x-7 15x≤25 [latex]x \leq \frac{5}{3} , x \leq 1 \frac{2}{3} ,  (-∞; 1(2/3))∩((2;7)∪(7;+∞)) Ответ: нет решения