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Консультация № 112171
03.12.2007, 18:15
0.00 руб.
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1
Увожаемые эксперты у меня имеется 10 уравнений на тему логарифмы, в которой я ничего не понимаю.Если бы вы помогли мне я был бы вам очень признанателен!
1. log(5-основание)log(7) 4x-1/x+7=0
2. log(2x+1) 4 + log(x-2/3) 4=0
3. (log(16) x^2-10*x+25) + (log(4) x+4) = (log(4) 26-4x)
4. 5*log(4) x + log(16) x - 4*log(64) x = 4
5. 3*log(5) x - 33*log(x) 5=-2
6. log(x) 3*x^2-4*x-16)=2
7.x*lg 5^x-1 - lg 25=0
8. log(3) 9^x -5*3^x + 21)=3
9. x^3*lg x+3 = 10000*x^2
10. (3x+1)^log(5) x-1 =x^2 - 2*x + 1
Вот вроде и все. Очень расчитываю на вашу помощь и поддержку уважаемые эксперты!
1. log(5-основание)log(7) 4x-1/x+7=0
2. log(2x+1) 4 + log(x-2/3) 4=0
3. (log(16) x^2-10*x+25) + (log(4) x+4) = (log(4) 26-4x)
4. 5*log(4) x + log(16) x - 4*log(64) x = 4
5. 3*log(5) x - 33*log(x) 5=-2
6. log(x) 3*x^2-4*x-16)=2
7.x*lg 5^x-1 - lg 25=0
8. log(3) 9^x -5*3^x + 21)=3
9. x^3*lg x+3 = 10000*x^2
10. (3x+1)^log(5) x-1 =x^2 - 2*x + 1
Вот вроде и все. Очень расчитываю на вашу помощь и поддержку уважаемые эксперты!
Обсуждение
Неизвестный
05.12.2007, 00:09
общий
это ответ
Здравствуйте, Мнекин Максим Валерьевич!
5. 3*log<sub>5</sub>x – 33*log<sub>x</sub>5 = -2.
Найдём ОДЗ:
x > 0, x≠1.
ОДЗ: x∈(0;1)∪(1;∞).
3*log<sub>5</sub>x – 33*log<sub>x</sub>5 = -2,
3*log<sub>5</sub>x – 33/log<sub>5</sub>x + 2 = 0,
{замена: t = log<sub>5</sub>x}
3t – 33/t + 2 = 0,
3t² + 2t – 33 = 0,
t<sub>1</sub> = -11/3, t<sub>2</sub> = 3.
t = -11/3 ⇒ log<sub>5</sub>x = -11/3 ⇒ x = 5<sup>-11/3</sup>;
t = 3 ⇒ log<sub>5</sub>x = 3 ⇒ x = 5³ = 125.
Ответ: x<sub>1</sub> = 5<sup>-11/3</sup>, x<sub>2</sub> = 125.
5. 3*log<sub>5</sub>x – 33*log<sub>x</sub>5 = -2.
Найдём ОДЗ:
x > 0, x≠1.
ОДЗ: x∈(0;1)∪(1;∞).
3*log<sub>5</sub>x – 33*log<sub>x</sub>5 = -2,
3*log<sub>5</sub>x – 33/log<sub>5</sub>x + 2 = 0,
{замена: t = log<sub>5</sub>x}
3t – 33/t + 2 = 0,
3t² + 2t – 33 = 0,
t<sub>1</sub> = -11/3, t<sub>2</sub> = 3.
t = -11/3 ⇒ log<sub>5</sub>x = -11/3 ⇒ x = 5<sup>-11/3</sup>;
t = 3 ⇒ log<sub>5</sub>x = 3 ⇒ x = 5³ = 125.
Ответ: x<sub>1</sub> = 5<sup>-11/3</sup>, x<sub>2</sub> = 125.
Форма ответа
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