1)log0,5(x^2+x)=-1
x^2+x > 0; x(x+1) >0; x < -1 и x > 0
x^2+x = 0,5^(-1)
x^2+x = 2
x^2+x - 2 = 0
x = -2 x = 1
2)2 log3 x=log3 (2x^2-x)
x > 0
2x^2-x >0; x(2x - 1) > 0; x< 0 и х > 0,5
log3 x^2 = log3 (2x^2-x)
x^2 = 2x^2 - x
x^2 - x = 0
x(x-1) = 0
x = 0 x = 1
х = 0 - не подходит
ответ: х = 1
3) 3)log7 (2-x)<=log7 (3x+6)</span>
2-x > 0; x < 2
3x+6 >0; x > -2
2-x <= 3x+6<br>4x >= -4
x >= -1
[-1;2)
4) log1/2(x^2-4)>log1/2 (x+2)-1
x^2-4 > 0; (x-2)(x+2) >0; x < -2 и x > 2
x + 2 > 0; x > -2
log1/2 (x^2-4)>log1/2 (x+2)-log1/2 1/2
log1/2(x^2-4)>log1/2 2(x+2)
x^2-4 < 2x + 4
x^2 - 2x -8 < 0
(x-4)(x+2) < 0
-2 < x < 4
ответ: (2;4)
5) lg^2x>=9
x > 0
lg^2x - 9 >= 0
(lgx -3)(lgx + 3) >= 0
lgx <= -3 и lgx >= 3
lgx <= lg 10^(-3) lgx >= lg 10^3
x <= 0,001 x >= 1000
ответ: (0;0,001] и [1000;+oo}