(у-2)(у+3)-(у-2)²≥6у-11
у²+3у-2у-6-у²+4у-4≥6у-11
5у-10≥6у-11
у≤1
у∈(-∞; 1]
1) Log3 4 - log3 16 + log3 4/9= Log3 4/ 16 + log3 4/9=Log3 ((4/16)*( 4/9))= Log3 1/9=
Log3 (3)^-2= -2
2) 2 log7 27 – log7 81-2 log7 21=log7 27^2 / 81-2 log7 21= log7 729/ 81- log7 21 ^2= log7 9- log7 21 ^2 = log7 (9/ 441)= log7 (1/ 49) = log7 (7^-2)=-2
3) 2 log2 8 +log2 15/4 – log2 15=log2 (8^2*(15/4)) – log2 15= log2 ((64*15)/4) – log2 15 =
log2 (16*15) – log2 15 = log2 ((16*15)/15)= log2 (16)= log2 (2^4)=4
4) log3 7 * log4 81 * log7 2= log4 81 * log7 2*1/ log7 3= log4 3^4 *( log7 2/ log7 3 )=
4* log4 3 * log3 2=4* log3 2*(1/ log3 4) = 4* log3 2*(1/ log3 2^2) = 4* log3 2*(1/ 2 log3 2)= (4* log3 2)/ (2 log3 2) =4/2=2
5) Lg3(log3 25+log3 2-log3 5) = Lg3(log3 (25* 2)-log3 5)= Lg3(log3 50/ 5) = Lg3*log3 10 = log10 3* log3 10= log10 3/ log10 3=1
1)8x=24
x=24:8
x=3
2.)8x=18:4
x=18.4:8
x=2.3
3)3x-5x=-2.5-4.5
-2x=-7
x=-7:(-2)
x=3.5
4)?не знаю
3x>-6
x(5-2√7)≥10-4√7
x>-2
x≤(10-4√7)/(5-2√7)- 5-2√7<0,поэтому знак неравенства поменялся
x>-2
x≤2(5-2√7)/(5-2√7)
x>-2
x≤2
целые корни:-1,0,1,2. т.е.,4 целых решения