Система уравнений 4^{x-1.5}+2^{x-2}=<1 log2((x−3)^2)+log√2(3−x)<12

Question

Система уравнений
4^{x-1.5}+2^{x-2}=<1<br> log2((x−3)^2)+log√2(3−x)<12

Answer 1

Log 2(x+1)=3
ОДЗ: х не = -1
2^3 = x+1
x=8-1=7

log 2(3x+4) = log 2(x+6)
ОДЗ: х не = -4/3 и не = -6
3x+4 = x+6
2x=2
x=1

log 2(x+1) = 1 + log2x
ОДЗ: х не = -1 и х не = 0
log 2(x+1) = log 2(2) + log2x
log 2(x+1) = log 2(2*2x)
x+1=4x
3x=1
x=1/3

log 0,1(x*2+3x) = -1
ОДЗ: х не = 0 и х не = -3
0,1^(-1) = x^2 + 3x
10 = x^2 + 3x
x^2 + 3x - 10 = 0
x(1) = -5
x(2) = 2