[tex] log_{3} (\frac{1}{x} +2)-log_{3}(x+4)\leq log_{3} (\frac{x+5}{x^{2}} ) [/tex]
Найти [tex] x [/tex]
Найти [tex] x [/tex]
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log3(1/x+2)/(x+4)≤log3(x+5)/x²
(1+2x)/(x+4)x≤(x+5)/x²
(x(1+2x)-(x+5)((x+4))/(x²(x+4)≤0
(x²-8x-20)/x²(x+4)≤0
(x-10)(x+2)/x²(x+4)≤0
x≠0;x≠-4
__-__-4__+__-2__-___10__+___
x€(-бес;-4)+[-2;0)+(0;10]
ОДЗ
1/х+2>0;(1+2х)/х>0;х€(-бес;-1/2)+(0;+бес)
х>-4
х+5/х²>0
х€(-5;0)+(0;+бес)
х€(-5;-1/2)+(0;+бес) это ОДЗ
ответ х€[-2;-1/2)+(0;10]