Question

lg^2(x^3)+3*lg(x^5)=6 пожалуйста помогите, срочно

Answer 1

1)ОДЗ x≠0
g²x³+3lgx^5=6
9lg²x+15lgx-6=0/3
3lg²x+5lgx-2=0
lgx=a
3a²+5a-2=0
D=25+24=49
a1=(-5-7)/6=-2⇒lgx=-2⇒x=0,01
a2=(-5+7)/6=1/3⇒lgx=1/3⇒x=∛10
2)ОДЗ x>0
(log(3)x+2)²+3log(3)x-12+20=0
log²(3)x+4log(30x+4+3log(3)x+8=0
log²(3)x+7log(3)x+12=0
log(3)x=a
a²+7a+12=0
a1+a2=-7 U a1*a2=12
a1=-4⇒log(3)x=-4⇒x=1/81
a2=-3⇒log(3)x=-3⇒x=1/27
3)ОДЗ x>0
1/3*log(5)x+2+9/log(5)x=-2/3*log(5)x+12
1/3*log²(5)x+2log(5)x+9+2/3*log²(5)x-12log(5)x=0
log²(5)x-10log(5)x+9=0
log(5)x=a
a²-10a+9=0
a1+a2=10 U a1*a2=9
a1=1⇒log(5)x=1⇒x=5
a2=9⇒log(5)x=9⇒x=5^9
4)2-1/(1-log(x²)3)=0
ОДЗ x≠0,x≠1,log(x²)3≠1⇒x≠+-√3
2-2log(x²)3-1=0
2log(x²)3=1
log(x²)3=1/2
x=3