高中数学对数及其运算课件北师大必修 22页

对数及其运算(1,2课时)学习内容1.对数的定义.2.对数的基本性质.3.对数恒等式.4.常用对数、自然对数的概念.5.对数的基本运算Evaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientProfile5.2.0.0.Copyright2004-2011AsposePtyLtd.\n思考问题一：假设2000年我国国民经济生产总值为a亿元,如果平均每年增长率为8.2%,求5年后国民经济生产总值是2000年的多少倍？答：y=a(1+8.2%)5=1.0825a是2000年的1.0825倍Evaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientProfile5.2.0.0.Copyright2004-2011AsposePtyLtd.\n思考问题二：假设2000年我国国民经济生产总值为a亿元,如果平均每年增长率为8.2%,问经过多少年后国民生产总值是2000年的2倍？答：a(1+8.2%)x=2ax=?1.082x=2Evaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientProfile5.2.0.0.Copyright2004-2011AsposePtyLtd.\n1.对数的定义：一般地，如果a(a>0,a≠1)的b次幂等于N，即ab=N,那么数b就叫做以a为底N的对数Evaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientProfile5.2.0.0.Copyright2004-2011AsposePtyLtd.\n表达形式abN对应的运算ab=N=alogaN=b底数方根底数指数根指数对数幂被开方数真数乘方，由a，b求N开方，由N，b求a对数，由a，N求b比较指数式、根式、对数式：（1）开方运算、对数运算都是指数运算的逆运算。（2）弄清对数式与指数式的互换是掌握对数意义及运算的关键Evaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientProfile5.2.0.0.Copyright2004-2011AsposePtyLtd.\n2.对数的基本性质:①零和负数没有对数.②loga1=0③logaa=1Evaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientProfile5.2.0.0.Copyright2004-2011AsposePtyLtd.\n3.对数恒等式：Evaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientProfile5.2.0.0.Copyright2004-2011AsposePtyLtd.\n4.常用对数与自然对数的定义:(1)以10为底的对数叫做常用对数.为了方便,N的常用对数log10N简记为:lgN.(2)以e为底的对数叫做自然对数.为了方便,N的自然对数logeN简记为:lnN.(e=2.71828…)Evaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientProfile5.2.0.0.Copyright2004-2011AsposePtyLtd.\n练习1.把下列指数式写成对数式：Evaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientProfile5.2.0.0.Copyright2004-2011AsposePtyLtd.\n练习2.把下列对数式写成指数式：Evaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientProfile5.2.0.0.Copyright2004-2011AsposePtyLtd.\n练习3.求下列各式的值：Evaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientProfile5.2.0.0.Copyright2004-2011AsposePtyLtd.\n练习4.计算下列各式的值:Evaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientProfile5.2.0.0.Copyright2004-2011AsposePtyLtd.\n例2求下列各式中x的值:Evaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientProfile5.2.0.0.Copyright2004-2011AsposePtyLtd.\n练习5.填空Evaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientProfile5.2.0.0.Copyright2004-2011AsposePtyLtd.\n(1)(2)(3)如果a>0,且a≠1,M>0,N>0,那么：对数运算性质如下：Evaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientProfile5.2.0.0.Copyright2004-2011AsposePtyLtd.\n例6、计算下列各式Evaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientProfile5.2.0.0.Copyright2004-2011AsposePtyLtd.\n例7用表示下列各式：(1)(2)例8求下列各式的值：(1)(2)Evaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientProfile5.2.0.0.Copyright2004-2011AsposePtyLtd.\n探究你能根据对数的定义推导出下面的换底公式吗？Evaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientProfile5.2.0.0.Copyright2004-2011AsposePtyLtd.\n不要产生下列的错误：Evaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientProfile5.2.0.0.Copyright2004-2011AsposePtyLtd.\n小结学习要求1.掌握指数式与对数式的互化.2.会由指数运算求简单的对数值.3.掌握对数恒等式及其应用.对数对数Evaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientProfile5.2.0.0.Copyright2004-2011AsposePtyLtd.\n本课学习的是对数的性质及运算法则，要求理解推出这些运算法则的依据和推导过程，会用语言叙述，要记住这些公式并能熟练应用。小结：Evaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientProfile5.2.0.0.Copyright2004-2011AsposePtyLtd.\n(1)(2)(3)如果a>0,且a≠1,M>0,N>0,那么：对数运算性质如下：Evaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientProfile5.2.0.0.Copyright2004-2011AsposePtyLtd.