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arturyo
@arturyo
August 2022
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Gviona
1)
a)log3(x)=2
x=3^2
x=9
^-знак степени
c) V(x-5)=-4
Решений нет,т.к. V(x-5)>=0
V-знак корня
2) a)log1/3(x-4)=1
log1/3(x-4)=log1/3(3)=x-4=3
x=7
b)3log4(x)=-6
log4(x)=-2
log4(x)=log4(1/16)
x=1/16
c)10 log3(x)+2=12
10 log3(x)=10
log3(x)=1
x=3
3) a)|x|=2
x=-2; x=2
b)|x|+1/6=1/3
|x|=1/3-1/6
|x|=1/6
x=-1/6; x=1/6
c)-4|x|+2=-8
-4|x|=-8-2
-4|x|=-10
|x|=2,5
x=-2,5; x=2,5
4)a)|x|=2 - уравнение на графике
x=-2; x=2
5)a)(x-2)^3=1
(x-2)^3=1^3
x-2=1
x=3
b)V(2x-3)=2
2x-3=2^2
2x-3=4
2x=7
x=3,5
c)10^(x-1)=0,01
10^(x-1)=10^-2
x-1=-2
x=-1
d)log25(x-3)=1/2
x-3= V25
x-3=5
x=8
e)|x+7/14|=-3/14
Решений нет,т.к.|x+7/14|>=0
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Answers & Comments
a)log3(x)=2
x=3^2
x=9
^-знак степени
c) V(x-5)=-4
Решений нет,т.к. V(x-5)>=0
V-знак корня
2) a)log1/3(x-4)=1
log1/3(x-4)=log1/3(3)=x-4=3
x=7
b)3log4(x)=-6
log4(x)=-2
log4(x)=log4(1/16)
x=1/16
c)10 log3(x)+2=12
10 log3(x)=10
log3(x)=1
x=3
3) a)|x|=2
x=-2; x=2
b)|x|+1/6=1/3
|x|=1/3-1/6
|x|=1/6
x=-1/6; x=1/6
c)-4|x|+2=-8
-4|x|=-8-2
-4|x|=-10
|x|=2,5
x=-2,5; x=2,5
4)a)|x|=2 - уравнение на графике
x=-2; x=2
5)a)(x-2)^3=1
(x-2)^3=1^3
x-2=1
x=3
b)V(2x-3)=2
2x-3=2^2
2x-3=4
2x=7
x=3,5
c)10^(x-1)=0,01
10^(x-1)=10^-2
x-1=-2
x=-1
d)log25(x-3)=1/2
x-3= V25
x-3=5
x=8
e)|x+7/14|=-3/14
Решений нет,т.к.|x+7/14|>=0