1) a) log(5) 125=log(5) (5^3)=3log(5) 5=3;
б) lg100=lg(10^2)=2lg10=2;
в) =3,
2)y=log(0,2) (x-1)
x-1>0; x>1 D(y)=(1;+∞)
3)log(2) (7-8x) =2
{7-8x>0
{7-8x=2^2; -8x=4-7; x=3/8; (7-8*(3/8)>0 верно )
Ответ. 3/8
4) log(2) (x-5)<2; 2=log(2) 2^2=log(2) 4<br> {x-5>0; {x>5
{x-5<4; {x<9 x⊂(5;9)<br> -------------
5) log(2) (x-2) + log(2) (x-3)=1
{x-2>0; {x>3 !!!
{x-3>0
{log(2) ((x-2)(x-3)) =log(2) 2; (x-2)(x-3)=2; x^2-5x+6-2=0
x^2-5x+4=0
D=25-16=9=3^2; x1=(5-3)/2=1; x2=4
Ответ.4
6) lg(x^2+2x+2)<1; 1=lg10<br> lg(x^2+2x+2){x^2+2x+2>0; D=4-8=-6; -6<0 корней нет, ветви параболы-вверх,(-∞;∞<br>{x^2+2x+2<10; x^2+2x-8<0; D=4-4*(-8)=4+32=36=6^2; x1=(-2-6)/2=-4;<br> x2=(-2+6)/2=2
+ - +
--------------(-4)----------------2----------------->x
////////////////////////// x⊂(-4;2)
Ответ. (-4;2)