1) lg x + lg (x-3)<1 ОДЗ х>0 , x-3>0 x>3
lg x*(x-3)<1<br> lg x²-3x <1<br> x²-3x < 10¹
x²-3x -10 <0<br> D=9+40=49
x=(3+7)/2=5
x=(3-7)/2=-2
+ - +
________-2____________5_____________
с учетом ОДЗ x∈(3 ;5)
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2) log₂ (x²-x-4)<3 ОДЗ x²-x-4>0
D=1+16=17
x₁=(1+√17)/2
x₂=(1-√17)/2
+ - +
_____________(1-√17)/2____________(1+√17)/2______
≈-1,05 ≈1,275
x²-x-4 <2³<br> x²-x-12<0<br>D=1+48=49
x=(1+7)/2=4
x=(1-7)/2=-3
+ - +
______-3__________4_________
c учетом ОДЗ (-3 ;(1-√17)/2)∪((1+√17)/2 ; 4)
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3) lg х >1/3
х> 10¹/₃
x∈(∛10 ;+∞)
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log₂x = 3log ₅x
log₂x = log₅x³ ОДЗ х>0
x=1