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aloloy
@aloloy
July 2022
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Решить 4 примера по теме "Степени и логарифмы". Буду очень благодарна за помощь.
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dtnth
Verified answer
5.58
3*2^x-2*2^x/2 -1=0
2^x/2=a
3a²-2a-1=0
D=4+12=16
a1=(2-4)/6=-1/3⇒2^x/2=-1/3-нет решения
a2=(2+4)/6=1⇒2^x/2=1⇒x/2=0⇒x=0
5.60
3^2x-2<5*3^x*2^x+2^2x=0 /2^2x≠0
(3/2)^2x-2,5*(3/2)^x+1=0
(3/2)^x=a
a²-2,5a+1=0
D=6,25-4=2,25
a1=(2,5-1,5)/2=1/2⇒(3/2)^x=1/2⇒x=log(1,5)0,5
a2=(2,5+1,5)/2=2⇒(3/2)^x=2⇒x=log(1,5)2
5.62
4*2^2x-2^x*3^x-18*3^2x=0 /3^2x≠0
4*(2/3)^2x-(2/3)^x-18=0(2/3)^x=a
4a²-a-18=0
D=1+288=289
a1=(1-17)/8=-2⇒(2/3)^x=-2-нет решения
a2=(1+17)/8=9/4⇒(2/3)^x=9/4⇒x=-2
5,64
2^12(x²+18)=2^28(x²+2x)
12(x²+18)=28(x²+2x)
3(x²+18)=7(x²+2x)
3x²+54=7x²+14x
7x²+14x-3x²-54=0
4x²+14x-54=0
2x²+7x-27=0
D=49+216=265
x1=(-7-√265)/4
x2=(-7+√265)/4
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Answers & Comments
Verified answer
5.583*2^x-2*2^x/2 -1=0
2^x/2=a
3a²-2a-1=0
D=4+12=16
a1=(2-4)/6=-1/3⇒2^x/2=-1/3-нет решения
a2=(2+4)/6=1⇒2^x/2=1⇒x/2=0⇒x=0
5.60
3^2x-2<5*3^x*2^x+2^2x=0 /2^2x≠0
(3/2)^2x-2,5*(3/2)^x+1=0
(3/2)^x=a
a²-2,5a+1=0
D=6,25-4=2,25
a1=(2,5-1,5)/2=1/2⇒(3/2)^x=1/2⇒x=log(1,5)0,5
a2=(2,5+1,5)/2=2⇒(3/2)^x=2⇒x=log(1,5)2
5.62
4*2^2x-2^x*3^x-18*3^2x=0 /3^2x≠0
4*(2/3)^2x-(2/3)^x-18=0(2/3)^x=a
4a²-a-18=0
D=1+288=289
a1=(1-17)/8=-2⇒(2/3)^x=-2-нет решения
a2=(1+17)/8=9/4⇒(2/3)^x=9/4⇒x=-2
5,64
2^12(x²+18)=2^28(x²+2x)
12(x²+18)=28(x²+2x)
3(x²+18)=7(x²+2x)
3x²+54=7x²+14x
7x²+14x-3x²-54=0
4x²+14x-54=0
2x²+7x-27=0
D=49+216=265
x1=(-7-√265)/4
x2=(-7+√265)/4