指對(duì)數(shù)函數(shù)的綜合應(yīng)用

1、第三講第三講指數(shù)和對(duì)數(shù)函數(shù)綜合問(wèn)題指數(shù)和對(duì)數(shù)函數(shù)綜合問(wèn)題【知識(shí)要點(diǎn)知識(shí)要點(diǎn)】1.有理數(shù)指數(shù)冪的運(yùn)算性質(zhì)：(1)；(2)；(3)；(4)；nmnmaaa???nmnmaaa??mnnmaa?)(mmmbaab?)(（5）；（6）；規(guī)定：.nnaa1??nmnmaa?)0(10??aa2.公式：.(4)，且?????????Nnnaannn100????。n。a。naann為偶數(shù)時(shí)當(dāng)為奇數(shù)時(shí)當(dāng)1?n.??Nn3.指數(shù)與對(duì)數(shù)的互化：；bNNa

2、ab???log4.對(duì)數(shù)的運(yùn)算性質(zhì)：，，)(logloglogMNNMaaa??)(logloglogNMNMaaa??常見(jiàn)的對(duì)數(shù)運(yùn)算公式：（1）loga1=0logaa=1(2)，logaaN=N=N（3）換底公式：logloglogmamNNa?5.兩大特殊對(duì)數(shù)（1）常用對(duì)數(shù)：（2）自然對(duì)數(shù)：性質(zhì)：性質(zhì)：6.指數(shù)函數(shù)與對(duì)數(shù)函數(shù)的圖象及性質(zhì)指數(shù)函數(shù)??01xyaaa???對(duì)數(shù)函數(shù)??log01ayxaa???題型一題型一指數(shù)與對(duì)數(shù)的運(yùn)

3、算指數(shù)與對(duì)數(shù)的運(yùn)算【例1】化簡(jiǎn)（1）；（2）)3()6)(2(656131212132bababa???；)00()(3421413223????baabbaabba（3）；（4）40lg50lg8lg5lg2lg???????222lg2lg2lg5lg22lg21.?????【例2】1求值：；4log35.02?2已知求的值.；3log2lognmaa??nma?23已知=14用a、b表示。35log28題型二題型二指數(shù)，對(duì)數(shù)比較大

4、小指數(shù)，對(duì)數(shù)比較大小【例3】已知，則的大小關(guān)系是（7.01.17.01.18.0log8.0log???cbacba）（A）（B）（C）（D）cba??cab??bac??acb??【例4】設(shè)cba均為正數(shù)，且aa21log2?，bb21log21???????，cc2log21???????.則（）A.cba??B.abc??C.bac??D.cab??題型三題型三解指數(shù)，對(duì)數(shù)不等式解指數(shù)，對(duì)數(shù)不等式【例5】設(shè)f(x)=12322lo