3
{log(8)(x+y)+log(8)(7+y)=1+log(8)5
ОДЗ x>-y U y>-7
log(8)[(x+y)(7+y)]=log(8)40
(x+y)(7+y)=40 (1)
2^log(2)(x-y)=4
x-y=4
x=4+y
подставим в 1
(4+2y)(7+y)=40
28+4y+14y+2y²-40=0
2y²+18y-12=0
y²+9y-6=0
D=81+24=105
y1=(-9-√105)/2 не удов усл
y2=(-9+√105)/2
x=4+(-9+√105)/2=(-1+√105)/2
4
lg(x-5)²+lg(x+6)²=2
ОДЗ
x≠5 U x≠-6
lg[(x-5)(x+6)]²=2
[(x-5)(x+6)]²=100
1)(x-5)(x+6)=-10
x²+x-30+10=0
x²+x-20=0
x1+x2=-1 U x1*x2=-20
x1=-5 U x2=4
2)(x-5)(x+6)=10
x²+x-30-10=0
x²+x-40=0
D=1+160=161
x3=(-1-√161)/2
x4=(-1+√161)/2
5
log(8)(x-1/x)+log(1/8)(1-x/6)≤1
ОДЗ
x-1/x>0⇒(x²-1)/x>0 x=-1 x=1 x=0
_ + _ +
---------------(-1)---------(0)----------(1)-----------------
-11
1-x/6>0⇒(6-x)/6>0⇒6-x>0⇒x<6<br>x∈(-1;0) U (1;6)
log(8)[(x²-1)/[]-log(8)[(6-x)/6]≤1
log(8)[6(x²-1)/x(6-x)]≤1
6(x²-1)/[x(6-x)]≤8
(6x²-6-48x+8x²)/[x(6-x)]≤0
(14x²-48x-6)/[x(6-x)]≤0
14x²-48x-6=0
7x²-24x-3=0
D=576+84=660
x1=(24-2√165)/14=(12-√165)/7
x2=(12+√165)/7
x=0
x=6
_ + _ + _
------[(12-√165)/7]------(0)------[(12+√165)/7]------------(6)------------
x<(12-√165)/7 U 0<x<(12+√165)/7 U x>6 +ОДЗ
x∈(-1;(12-√165)/7] U (1;(12+√165)/7]