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Rauau1999
@Rauau1999
June 2022
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Решить неравенство:
5^(-3x)+5^(1-3x)+5^(-3x-3) < 30,04
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scorostnaja
Вводится новая переменная...и решается уравнение
1 votes
Thanks 0
uekmyfhfp
5^(-3x) + 5^(1-3x) + 5^(-3x -3) < 30,04;
5^(-3x - 3 + 3) + 5^(-3x -3 + 4) + 5^(- 3x - 3) < 30,04;
5^(-3x - 3) * 5^3 + 5^(-3x - 3) *5^4 + 5^(-3x - 3) < 30,04;
5^(-3x - 3) * 125 + 5^(-3x - 3) * 625 + 5^(-3x - 3) < 30,04;
5^(-3x - 3)* (125 + 625 + 1) < 30,04;
5^(-3x - 3) * 751 < 30,04;
5^(-3x - 3) < 30,04 :751 ;
5^(-3x - 3) < 0,04; 0,04 = 4/100 = 1/25 = 5^(-2);
5^(- 3x - 3) < 5^(-2);
5 > 1; ⇒
- 3x - 3 < - 2;
- 3x < 1; /-3 < 0;
x > - 1/3
0 votes
Thanks 0
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Answers & Comments
5^(-3x - 3 + 3) + 5^(-3x -3 + 4) + 5^(- 3x - 3) < 30,04;
5^(-3x - 3) * 5^3 + 5^(-3x - 3) *5^4 + 5^(-3x - 3) < 30,04;
5^(-3x - 3) * 125 + 5^(-3x - 3) * 625 + 5^(-3x - 3) < 30,04;
5^(-3x - 3)* (125 + 625 + 1) < 30,04;
5^(-3x - 3) * 751 < 30,04;
5^(-3x - 3) < 30,04 :751 ;
5^(-3x - 3) < 0,04; 0,04 = 4/100 = 1/25 = 5^(-2);
5^(- 3x - 3) < 5^(-2);
5 > 1; ⇒
- 3x - 3 < - 2;
- 3x < 1; /-3 < 0;
x > - 1/3