68
log(0,7)7^(5x/14)>log(0,7)7^(2,5)
7^(5x/14)<7^(5/2)<br>5x/14<5/2<br>x<5/2:5/14<br>x<7<br>x∈(-∞;7)
69
ОДЗ
x>0;4-x>0⇒x<4;x-1≠0⇒x≠1;10-x>0⇒x<10<br>x∈(0;1) U (1;4)
log(3)x²+log(3)(4-x)≤log(3)(x-1)²+log(3)(10-x)
log(3)x²(4-x)≤log(3)(x-1)²(10-x)
x²(4-x)≤(x-1)²(10-x)
4x²-x³-10x²+x³+20x-2x²-10+x≤0
8x²-21x+10≥0
D=441-320=121
x1=(21-11)/16=5/8
x2=(21+11)/16=2
x≤5/8 U x≥2
x∈(0;5/8] U [2;4)
70
ОДЗ
{x(x-2)/(x-3)>0
{log(8)x(x-2)/(x-3)>0⇒x(x-2)/(x-3)>1⇒
x(x-2)/(x-3)>1
(x²-2x-x+3)/(x-3)>0
(x²-3x+3)/(x-3)>0
x²-3x+3>0 при любом х,т.к. D=-3<0⇒x-3>0⇒x>3
x∈(3;∞)
log(8)x(x-2)/(x-3)>1
x(x-2)/(x-3)>8
(x²-2x-8x+24)/(x-3)>0
(x²-10x+24)/(x-3)>0
x²-10x+24=0
x1+x2=10 U x1*x2=24⇒x1=4 u x2=6
x-3=0⇒x=3
_ + _ +
----------(3)---------(4)--------------(6)-----------------
36
x∈(3;4) U (6;∞)