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shpont
@shpont
August 2022
2
6
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помогите пож-та!!Очень срочно!!
Решите какие сможете,спасибо!
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sedinalana
Verified answer
1
а)(6²)^3/2+(4³)^2/3-(25²)^1/2=6³+4³-25=216+16-25=207
б)(2³)^1/3*2^-1=2*1/2=1
в)3*3^log(3)8=3*8=24
2
lgx=lg(√3*5/∛4)
x=5√3/∛4
3
a)(3^-4)^(3x-2)=(3³)^(x+3)
3^(-12x+8)=3^(3x+9)
-12x+8=3x+9
-12x-3x=9-8
-15x=1
x=-1/15
б)ОДЗ
4-2x>0⇒x<2
log(3)[(4-2x)/2]=2
log(3)(2-x)=2
2-x=9
x=2-9
x=-7
1 votes
Thanks 2
sedinalana
4,5,6 задай другим вопросом и я напишу решение
oganesbagoyan
Verified answer
4.
a) (1/64) ^ x ≤ √(1/8) ;
(1/8) ^(2x) ≤
(1/8) ^ (1/2) ;
2x
≥
1/2 ;
x ≥ 1/4 иначе x ∈ [ 0,25 ; ∞) .
---
b) Log2 (x -5) / (x-4) < 1 ;
Log2 (x -5) / (x-4) < Log2 2⇔ 0 < (x -5) / (x-4) < 2 ;
{ (x-5) / (x-4) >0 ; 2 -(x -5) / (x-4) >0
⇔
{ (x -4) (x-5) > 0 ; (x - 3)(x -4) >0 ⇒x ∈ (-∞ ; 3) u (5 ; ∞) .
5
.
(8x² -2x -1 ) / x ≤ 0 ;
(8(x +1/4)(x- 1/2) / x ≤ 0 ;
- + - +
//////////////// [ -1/4 ] ----------- (0) ///////////// [1/2] ------------
⇒ x∈(-∞ ; -0,25] U (
0 ; 0,5] .
6
.
√(x-4) + √(x+24) = 14 ; ОДЗ : x∈ [ 4 ; ∞) .
x+10 +√(x-4)(x+24) =98 ;
√(x-4)(x+24) = 88 -x ; * * * x
≤ 88 * * *
(x-4)(x+24) = (88 -x) ²
x
² +20x-96=
88
² - 176x +x² ;
196x = 88
² +96 ;
x
=(7744+96) /196 = ( 7744+96) /196 =7840 / 196
= 40
.
0 votes
Thanks 1
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Answers & Comments
Verified answer
1а)(6²)^3/2+(4³)^2/3-(25²)^1/2=6³+4³-25=216+16-25=207
б)(2³)^1/3*2^-1=2*1/2=1
в)3*3^log(3)8=3*8=24
2
lgx=lg(√3*5/∛4)
x=5√3/∛4
3
a)(3^-4)^(3x-2)=(3³)^(x+3)
3^(-12x+8)=3^(3x+9)
-12x+8=3x+9
-12x-3x=9-8
-15x=1
x=-1/15
б)ОДЗ
4-2x>0⇒x<2
log(3)[(4-2x)/2]=2
log(3)(2-x)=2
2-x=9
x=2-9
x=-7
Verified answer
4.a) (1/64) ^ x ≤ √(1/8) ;
(1/8) ^(2x) ≤ (1/8) ^ (1/2) ;
2x≥ 1/2 ;
x ≥ 1/4 иначе x ∈ [ 0,25 ; ∞) .
---
b) Log2 (x -5) / (x-4) < 1 ;
Log2 (x -5) / (x-4) < Log2 2⇔ 0 < (x -5) / (x-4) < 2 ;
{ (x-5) / (x-4) >0 ; 2 -(x -5) / (x-4) >0 ⇔
{ (x -4) (x-5) > 0 ; (x - 3)(x -4) >0 ⇒x ∈ (-∞ ; 3) u (5 ; ∞) .
5.
(8x² -2x -1 ) / x ≤ 0 ;
(8(x +1/4)(x- 1/2) / x ≤ 0 ;
- + - +
//////////////// [ -1/4 ] ----------- (0) ///////////// [1/2] ------------
⇒ x∈(-∞ ; -0,25] U ( 0 ; 0,5] .
6.
√(x-4) + √(x+24) = 14 ; ОДЗ : x∈ [ 4 ; ∞) .
x+10 +√(x-4)(x+24) =98 ;
√(x-4)(x+24) = 88 -x ; * * * x ≤ 88 * * *
(x-4)(x+24) = (88 -x) ²
x² +20x-96= 88² - 176x +x² ;
196x = 88² +96 ;
x =(7744+96) /196 = ( 7744+96) /196 =7840 / 196 = 40 .