1
a^log(b)x=x^log(b)a⇒5^log(2)x=x^log(2)5
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5^log(2)x+2*5^log(2)x=15
3*5^log(2)x=15
5^log(2)x=5
log(2)x=1
x=2
2
ОДЗ
4x-x²>0
x(4-x)>0
x=0 x=4
x∈(0;4)
log(1/3)(4x-x²)=a
a²-1>0
(a-1)(a+1)>0
a=1 a=-1
a<-1⇒log(1/3)(4x-x²)<-1<br>4x-x²>3 (основание меньше 1,знак меняется)
x²-4x+3<0<br>x1+x2=4 U x1*x2=3⇒x1=1 U x2=3
1a>1⇒log(1/3)(4x-x²)>1
4x-x²<1/3<br>x²-4x+1/3>0
3x²-12x+1>0
D=144-12=132
√D=2√33
x1=(12-2√33)/6=(6-√33)/3
x2=(6+√33)/3
x<(6-√33)/3 U x>(6+√33)/3
x∈(0;(6-√33)/3) U (1;3) U ((6-√33)/3;4)