Question

log2 (x+1)+ log2 (3x-1)>log2 (9x+5)

Answer 1

log2(x+1)+log2(3x-1)>log2(9x+5)
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ОДЗ:
{x+1>0;  x>-1
{3x-1>0; x>1/3
{9x+5>0; x>-5/9
Решение ОДЗ: x e (1/3; + беск.)
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log2(x+1)(3x-1)> log2(9x+5)
(x+1)(3x-1)>9x+5
3x^2-x+3x-1-9x-5>0
3x^2-7x-6>0
3x^2-7x-6=0
D=(-7)^2-4*3*(-6)=121
x1=(7-11)/6=-2/3;  x2=(7+11)/6=3
___+______(-2/3)____-____(3)_____+_____
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С учетом ОДЗ: x e (3; + беск.)