Урок повторение . Алгебра и начала анализа 11 класс.
Тема урока: Решение логарифмических уравнений
Цель урока: 1) Повторить свойства логарифмов
2) Повторить решение простейших логарифмических уравнений
3) Разобрать решение логарифмических уравнений С1
План
1. Организационный момент
2. Устно:
1) Свойства логарифмов
а)
+
=
б)
-
= ![](https://fsd.videouroki.net/html/2015/04/09/98709356/98709356_6.png)
в)
= 0
г)
= 1
д)
= p ![](https://fsd.videouroki.net/html/2015/04/09/98709356/98709356_10.png)
е)
=
![](https://fsd.videouroki.net/html/2015/04/09/98709356/98709356_10.png)
ж)
= ![](https://fsd.videouroki.net/html/2015/04/09/98709356/98709356_15.png)
3. 2) Вычислить.
1)
6) ![](https://fsd.videouroki.net/html/2015/04/09/98709356/98709356_17.png)
2)
+
7)
+ ![](https://fsd.videouroki.net/html/2015/04/09/98709356/98709356_21.png)
3)
-
8) ![](https://fsd.videouroki.net/html/2015/04/09/98709356/98709356_24.png)
4)
9) ![](data:image/png;base64,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)
5)
10) ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAB4AAAATCAIAAAAIzCorAAABdElEQVR4nGP5//8/A20AC43MHR5Gv337dvXq1Zs3b966dSuVjebg4ODh4dm+fTvl5qIbzc3NbWJiQhVz0Y0GAkZGRloZDQezZs2aOXNmV1cXkLFz587c3Nzm5masKnft2vX06dP79+8/evRowYIFhI0ODQ3NyMg4e/bs8uXLgZp9fHzKysp4eXnRlAHt+/DhQ29v76pVq1auXEmUqwUFBYGkv78/ExOTq6vrv3//nj9/jmY0MCEBjTtz5syxY8eAdiA7GZ/RyICZmRlIYhYJlZWVFhYWM2bMYGNjO378ODB1kWw0VvDu3bsrV64cOHBASEgIqwJ0o//8+QMkgd5HFvz9+zemIAsLC9A3wMgABtfPnz/XrFnj6+vLx8eH3WhgaE6fPh3ImDhxIsT7S5YsKSkpAXqZAZxmOjo62NnZIYqBpgDTT2RkJDA+NDQ0srOzubi4cLpaUlJyChhAuEVFRRBGORhgerkQDLCGBpYAoSIYmkYDAFVZmLfecjN1AAAAAElFTkSuQmCC)
3. Решим в классе
а)
= 3 ОДЗ.
1 – 2x = 2 3
1 -2x = 8
-2x = 7
X = - 3, 5
Ответ: - 3,5
б) =
ОДЗ.
x ϵ ( 0,4; +∞)
5x – 2 = x + 4
4x = 6
x = ![](data:image/png;base64,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)
x = 1, 5
Ответ: 1, 5
в) = x + 10 ОДЗ.
3x – 4 = x + 10
2x = 14
X = 7
Ответ: 7
г)
ОДЗ. ![](data:image/png;base64,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)
5x – 5 = 10
5x = 15
X = 3
Ответ: 3
д) ОДЗ.
![](data:image/png;base64,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)
2x + 5 = 6
2x = 1
x = 0, 5
Ответ: 0, 5
4. Слабые ученики получают карточки и решают самостоятельно:
Карточка № 1
Решите уравнение а)
б)
в) ![](data:image/png;base64,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)
г)
д) lg (x + 1) = 1 + lg x
Карточка № 2
Решите уравнение а) ![](data:image/png;base64,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)
б)
в) ![](data:image/png;base64,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)
г)
д)
Карточка № 3
Решите уравнение а) ![](data:image/png;base64,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)
б)
в)
г)
д)
Карточка № 4
Решите уравнение а) ![](data:image/png;base64,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)
б)
в) ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAGsAAAAWCAIAAABIYfVEAAAEhUlEQVR4nO2YaSh1WxjHDUeGIsocJTMZMh5CinwwRDLcQuYoCiXpuERCbkiGJBTKFzNliPLJkHxDMmcsZMpYEu7/WrU7jn2cvZ29733d3v+H3dqrtZ+1128/63metQVvb28KvGl3d9fCwuJXNii/BPyZfnh46OvrE4lEHNrs7e3Ny8vT0NDg0KacYkpwfn6+oaEBRJibbmtrc3Z2RuP4+Li5uXlpacnf37+0tJS5hdnZ2erq6pWVlbq6utjYWPTAYGdnZ3Z2NnMjfIspQaFQODAwwMr0xMREREQEGvf39wBxdHTk7u7OiuDNzc34+PjU1FRCQgIhaGtr29jY+CMJCgT/jNzc3MSSLC0tx8bG8vPzjY2NQcTIyOju7i4jI8PExET8kbW1NQMDA4X3ZeMKEHAfVi8XHByMq4uLCyYiPYaGhqurq6yM8C12cTA1NbW7uxsEtbW1U1JSsrKy1NTU4uLi4Fzl5eUSg6+urtTV1UkbQaC2tjYgICAkJAS3t7e3OTk5aO/v70dGRlpZWenp6V1eXlLPIl1sb28rKyujjW9WXFxM+mEQZr+9Wj7EjuDy8jKWioabmxt8wc/Pr7+/f25uDjRpTAsEr6+vSkpKaPv4+AwPD2N8S0sLbrW0tDIzMwEdO11RURE95+fntDOenp5eXFxQ9l9eXlRUVFi9M9+SShBLcnBwODs7E++Er4FXaGjozs6Or6+vrq5uWFjYH++ixsCtRkZGkDHB+vHxEbBIv46Ojrm5OTUMboj4SPBJE7I5HLCgoABthFFTU1MYxKTfW6qcogWi8AVBhDlxv1hcXMQ1NzcXdOBZe3t7SLUIi4WFhfX19Y6Ojl1dXdhiWOH19fXT0xMGe3h4IAvb29tXVVUhJ5iZmWEM+uFTra2tiYmJNjY2yNFIC7Qc4W7R0dF4EE8BNykDYBBmOeDBXhJAKNET7Onp8fLywpXqwS3AoYGwRXXC0bAwb2/voaGhjY0NhHzkCkRGFC6ACMdEIQKCRUVF4sbhRCSudXR0fPHGCIKTk5MSnTAYExMjY6086DMQSjQE8Z23trbi4+Nl2nV1dUWEggcBJfChh9QZ8DJVVdWoqKimpia5X/6DsIkwF7c2iRCviYt81tdAJAnikPfXuxB3ZM7657s+92Nrk0ZycrJMI6yUlpZGtWdmZoKCgmiHwX+fn5+pW/hyZWWlk5MT8lhNTc3o6Oj09DTDg41MIJIEEd0Am6tjk6amJid2aA0GBgZK8xoJoa5E6ispKUHAQZFPUhNDyQTygSCmwQbEhmc+wU9ReHg40iCIW1tbi/eTYkuiTX0YJkA+EGxvb8fRjcRLkk/t7OyQEMrKyjhYxH8qnJdQTolvbSIKFm0cZALkA0Gy4UkblQpGr6+vc7kOTsU8DkLIaShmFxYW0tPTmU/BBAiPf7f4FvM4ODg4iEOUvr4+6qqTk5PDw0OhUMjVa/xggkyEyjQpKamiogIHSpTlIpEIEGnrUIYf47OkEsSB4dtGfx15enpS+w7ny4ODg2+bkgbkf+6D/4J+E5RXvwnKq78BSu41uLO3Dg0AAAAASUVORK5CYII=)
г) 2 + ![](data:image/png;base64,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)
д)
5. С сильными учениками решим уравнение
а)
Перейдем к основанию 3
= x = - 3
Ответ: - 3
б) ОДЗ.
Решение
1 +
3 + 4x2 = 2*(3 – 4x2) = 3 – 4x2 0 , т.к. 3 + 4x2 2
4x2 = 1
X = ![](data:image/png;base64,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)
Ответ: ![](data:image/png;base64,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)
6. Тетради с самостоятельными работами собрать
7. Домашние задание
1) Карточки
2) Учебник № 524 (а,б)
№ 523 (а,б)
Литература:
Тестовые задания по алгебре и началом анализа.
Базовый уровень сложности
Е. А. Семенко Просвещение – 10г.
Краснодар 2005 г.
И. Н. Сергеев , В.С. Понферов ЕГЭ 1000 задач С1 – С6
Математика Издательство
«Экзамен» Москва 2013 г.
Алгебра и начало анализа
Учебник для 10 -11 классов общеобразовательных учреждений
Под редакцией А. Н. Коммогорова Москва
«Просвещение» 2011 г.