Ответ:
4. a) 5^(-0,6x-3) =5^2
-0,6x-3=2
-0,6x=2+3
-0,6x=5
x= -25/3 или -8,3 или -8 1/3
4. б) log2 (2x-4)=7, x>2
log2 (2(x-2))=7
log2 (2)+log2 (x-2)=7
1+log2 (x-2)=7
log2 (x-2)=7-1
log2 (x-2)=6
x-2=2^6
x-2=64
x=64+2
x=66, x>2
x=66
5. a) log1/2 (2x+5)>-3, x> -5/2
2x+5<(1/2)^-3</strong>
2x+5<2^3</strong>
2x+5<8</strong>
2x<8-5</strong>
2x<-3</strong>
x< 3/2, x> -5/2
x ∈ (-5/2, 3/2)
5. б) 1/(4)^x -2*2^(-x) -8<0</strong>
1/(2^2)^x -2*1/(2)^x -8<0</strong>
2^x < -1/2
2^x >1/4
x ∈ (-2, + ∞)
Объяснение:
5. в) x^2 +2x-3/(x-7)*(x+5) <0</strong>
x^2 +3x-x-3/(x-7)*(x+5) <0</strong>
x ∈ (-5, -3) ∪ (1, 7)