Task/26102912
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2)
Lg(3x+5/2) = -Lg(3x+1) ;
ОДЗ: 3x+5/2 >0 и 3x +1 > 0 ⇔x > - 1/3.
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Lg(9x+5)/2 +Lg(3x+1) =0 ;
Lg(9x+5) - Lg2 +Lg(3x+1) =0 ;
Lg(9x+5)+Lg(3x+1)= Lg2 ;
Lg ( (9x +5) (3x+1) ) =lg 2 ;
(9x +5) (3x+1) =2 ;
27x² +24x -3 =0 ;
9x² +8x -1 = 0 ; D₁=4² -9*(-1) =25 =5²
x₁=(-4 -5) /9 = -1 ∉ ОДЗ ;
x₂ =(-4+5) /9 =1/9.
ответ : 1/9 .
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3)
Lg³ x² = 8 Lgx ;
ОДЗ: x > 0
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(Lg x²)³ = 8 Lgx ;
(2Lg x)³ = 8 Lgx ;
8Lg³ x = 8 Lgx ; * * * Lgx =t ; t³ -t =0 * * *
Lgx *(Lg² x - 1) =0 ;
Lgx *(Lg x - 1)*(Lgx +1) =0 ;
Lgx =0 ⇒ x =1;
Lg x - 1=0 ⇒ x =10;
Lg x + 1=0 ⇒ x =1/10.
ответ : {1/10 ;1;10} . * * * 10⁻¹ ; 10⁰ ;10¹ * * *
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1.
13^(2x -1) <1 ;
13^(2x -1) < 13⁰ ; * * * 13 >1 * * *
2x -1 <0 ;
x <0,5 .
ответ : x ∈(-∞; 0,5).
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3.
2^(8-x) +7^(3-x) ≥ 7^(4-x) +11*2^(3-x) ; ||* (2^x) *(7^x)
2⁸ *7^x +7³2 ^x ≥7⁴*2^x +11*2³*7^x ;
2³ *(7^x ) ( 2⁵ -11) ≥ (7³)*(2^x)*(7-1) ;
8*21*(7^x ) ≥ (7³)*6*(2^x) ;
4*(7^x ) ≥ 7²*(2^x) ;
(7^x ) / (2^x) ≥ 7² / 2² ;
(7 / 2) ^x ≥ (7 / 2)² * * * 7/2 >1 * * *
x ≥ 2
ответ : x ∈[ 2; ∞).
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Удачи !
(-2)³ -8 -8*3 -24
----- = ------ = -------- = --------
-2+1/3 -2+1/3 -6+1 -5
=4,8
1.
a) 1.25^4 x 8^4
=(1.25 x 8)^4
=10^4
b) 6^12/36 x 6^9
=6^3/6^2
=6
2.
a) 21x^3y^2 x (-4/7x)
=-3x^3y^2 x 4x
= -12x^4y^2
b) -0.25a^2b^4 x (-8ba^3)
=-0.25a^2b^4 x (-8a^3b)
=2a^5b^5
3.
a) -3a^8b^3 x 2ab^6
=-6a^8b^3+6a^1
=-6a^8+1b^9
=-6a^9b^9
b) -98xy^3 x (1/7x^2)^2
=-98xy^3 x 1/49x^4
=-2xy^3x^4
=-2x^5y^3
c) (-4ab^3)^3 x (a^2b)^2
=-(4ab^3)^3 x (a^2b)^2
=-64a^3b^9a^4b^2
=-64a^7b^11
4. ?
5.
3 x 3^3 x -1/3^2
=-3 x 3^3 x 3^-2
=-3^2
=-9