Предмет: Математика, автор: natoki

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Ответы

Автор ответа: bilivam100

Ответ:

1,2. смотри ниже.

3. А) 46. Б) 3. В) решений нет. Г) 1/3, 27.

Пошаговое объяснение:

1. Уравнение, содержащее неизвестное под знаком логарифма или (и) в его основании, называется логарифмическим уравнением.

Применение определения логарифма

Метод потенцирования

Применение основного логарифмического тождества

Метод введения новой переменной

Метод логарифмирования

А) $x+3=7^{2} , x+3=49, x=46.$

Ответ: 46.

Б) ОДЗ:

$\left \{ {{x>2} \atop {x>-6}} \right.$ x∈(2; +∞)

$log_{3}(x-2)(x+6)=2,\\x^{2} +4x-12=9,\\x^{2} +4x-21=0,\\x_{1}=-7, x_{2}=3.$

Ответ: 3.

В)

$\left \{ {{5x+3>0} \atop {5x+3=7x+5}} \right. \\\left \{ {{5x>-3} \atop {2x=-2}} \right. \\\left \{ {{x>-\frac{3}{5} } \atop {x=-1}} \right.$

Ответ: нет решений.

Г) ОДЗ: x>0, x∈(0; +∞)

Пусть $log_{3}x=t$ .

$t^{2} -2t-3=0,\\t_{1}=-1, t_{2}=3.$

$log_{3}x=-1, x=\frac{1}{3} .\\log_{3}x=3, x=27.$

Ответ: 1/3, 27.

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