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1)x>0
log²(5)x-1/log(5)x=2
log(5)x≠0⇒x≠1
log³(5)x-2log(5)x-1=0
log(5)x=a
a³-2a-1=0
a=-1 -1+2-1=0
a³-2a-1 /a+1
a³+a² a²-a-1
---------
-a²-2a
-a²-a
-------------
-a-1
-a-1
---------
0
log(5)x=1⇒x=5
a²-a-1=0
D=1+4=5
a1=(1-√5)/2⇒log(5)x=(1-√5)/2⇒x=![5^{(1- sqrt{5})/2 } 5^{(1- sqrt{5})/2 }](https://tex.z-dn.net/?f=+5%5E%7B%281-+sqrt%7B5%7D%29%2F2+%7D+)
a2=(1+√5)/2⇒log(5)x=(1+√5)/2⇒x=![5 ^{(1+ sqrt{5})/2 } 5 ^{(1+ sqrt{5})/2 }](https://tex.z-dn.net/?f=5+%5E%7B%281%2B+sqrt%7B5%7D%29%2F2+%7D+)
2)x>0 U y>0
x=7-y
lg(7-y)+lgy=1
lg(7y-y²)=1
7y-y²=10
y²-7y+10=0
y1+y2=7 U y1*y2=10
y1=2⇒x1=7-2=5
y2=5⇒x2=7-5=2
3)x+1>0⇒x>-1
log(4)(x²+8)/(x+1)=log(4)8
(x²+8)/(x+1)=8
x²+8=8x+8
x²-8x=0
x(x-8)=0
x=0 x=8
log²(5)x-1/log(5)x=2
log(5)x≠0⇒x≠1
log³(5)x-2log(5)x-1=0
log(5)x=a
a³-2a-1=0
a=-1 -1+2-1=0
a³-2a-1 /a+1
a³+a² a²-a-1
---------
-a²-2a
-a²-a
-------------
-a-1
-a-1
---------
0
log(5)x=1⇒x=5
a²-a-1=0
D=1+4=5
a1=(1-√5)/2⇒log(5)x=(1-√5)/2⇒x=
a2=(1+√5)/2⇒log(5)x=(1+√5)/2⇒x=
2)x>0 U y>0
x=7-y
lg(7-y)+lgy=1
lg(7y-y²)=1
7y-y²=10
y²-7y+10=0
y1+y2=7 U y1*y2=10
y1=2⇒x1=7-2=5
y2=5⇒x2=7-5=2
3)x+1>0⇒x>-1
log(4)(x²+8)/(x+1)=log(4)8
(x²+8)/(x+1)=8
x²+8=8x+8
x²-8x=0
x(x-8)=0
x=0 x=8
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