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zigor3262
@zigor3262
September 2021
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m11m
3.
0,8^(0.8-5x)=0.5√5
(4/5)^(0.8-5x)=
√5
2
(4/5)^(0.8-5x) = (5/4)^(1/2)
(4/5)^(0.8-5x)=(4/5)^(-1/2)
0.8-5x=-1/2
0.8-5x= -0.5
-5x= -0.5-0.8
-5x= -1.3
x= -1.3 : (-5)
x= 0.26
Ответ: 0,26
4. 4^((x+3)/x) + 4^((2x+3)/x) = 320
ОДЗ: x≠0
2x+3
=
x+x+3
= 1 +
x+3
x x x
4^((x+3)/x) + 4^(1 + (x+3)/x)=320
4^((x+3)/x) (1+4)=320
4^((x+3)/x)=320 : 5
4^((x+3)/x)=64
4^((x+3)/x)=4³
x+3
= 3
x
x+3=3x
x-3x= -3
-2x= -3
x=1.5
Ответ: 1,5
5. 36^(x)-13*6^(x)+36=0
Замена 6^(x)=y 36^(x)=(6²)^(x)=(6^(x))²=y²
y²-13y+36=0
D=169-144=25
y₁=
13-5
= 4
2
y₁=
13+5
=9
2
При у=4
6^(x)=4
x=log₆ 4
При у=9
6^(x)=9
x=log₆ 9
log₆ 4 + log₆ 9 = log₆ (4*9)=log₆ 36 = log₆ 6² = 2
Ответ: 2.
2 votes
Thanks 1
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Answers & Comments
0,8^(0.8-5x)=0.5√5
(4/5)^(0.8-5x)=√5
2
(4/5)^(0.8-5x) = (5/4)^(1/2)
(4/5)^(0.8-5x)=(4/5)^(-1/2)
0.8-5x=-1/2
0.8-5x= -0.5
-5x= -0.5-0.8
-5x= -1.3
x= -1.3 : (-5)
x= 0.26
Ответ: 0,26
4. 4^((x+3)/x) + 4^((2x+3)/x) = 320
ОДЗ: x≠0
2x+3 = x+x+3 = 1 + x+3
x x x
4^((x+3)/x) + 4^(1 + (x+3)/x)=320
4^((x+3)/x) (1+4)=320
4^((x+3)/x)=320 : 5
4^((x+3)/x)=64
4^((x+3)/x)=4³
x+3 = 3
x
x+3=3x
x-3x= -3
-2x= -3
x=1.5
Ответ: 1,5
5. 36^(x)-13*6^(x)+36=0
Замена 6^(x)=y 36^(x)=(6²)^(x)=(6^(x))²=y²
y²-13y+36=0
D=169-144=25
y₁=13-5 = 4
2
y₁= 13+5 =9
2
При у=4
6^(x)=4
x=log₆ 4
При у=9
6^(x)=9
x=log₆ 9
log₆ 4 + log₆ 9 = log₆ (4*9)=log₆ 36 = log₆ 6² = 2
Ответ: 2.