Question

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

Answer 1

{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

Answer 2

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