(Используем свойства логарифма).
![log_{15}log_{5}log_{2}32=log_{15}log_{5}log_{2}2^5=log_{15}log_{5}(5log_{2}2)= \\ \\ =log_{15}log_{5}(5*1)=log_{15}log_{5}5=log_{15}1=0](https://tex.z-dn.net/?f=log_%7B15%7Dlog_%7B5%7Dlog_%7B2%7D32%3Dlog_%7B15%7Dlog_%7B5%7Dlog_%7B2%7D2%5E5%3Dlog_%7B15%7Dlog_%7B5%7D%285log_%7B2%7D2%29%3D+%5C%5C++%5C%5C+%3Dlog_%7B15%7Dlog_%7B5%7D%285%2A1%29%3Dlog_%7B15%7Dlog_%7B5%7D5%3Dlog_%7B15%7D1%3D0)
1
x>0
log(3)x=a
3a²+a-4=0
D=1+48=49
a1=(-1-7)/6=-4/3⇒log(3)x=-4/3⇒x=1/3∛x
a2=(-1+7)/6=1⇒log(3)x=1⇒x=3
2
{log(13)(x²+y²)=2⇒x²+y²=169
{log(5)x-log(5)y=log(5)5-log(5)12⇒log(5)(x/y)=log(5)(5/12)⇒x/y=5/12
12x=5y
y=2,4x
x²+(2,4x)²=169
x²+5,76x²=169
6,76x²=169
x2=169/6,76
x=-13/2,6=-5⇒y=2,4*(-5)=-12
x=13/2,6=5⇒y=2,4*5=12
(-5;-12);(5;12)
X²+y²=9
x²+y²=r²
r²=9
r=3
Координаты центра (0;0).
Раскрываем скобки
x^2-10x+25-10x-x^2= -20x+25
Подставляем x
-20 (-1/20)+25=26
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-1
4
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