当前位置:首页 >> 高二数学 >>

2016高中数学第二章指数函数、对数函数和幂函数2.2.2换底公式课件湘教版必修1_图文

第2章—— 2.2 对数函数 2.2.2 [学习目标] 换底公式 1.能记住换底公式,并会证明换底公式. 2.会利用换底公式解决一些对数式的化简、求值、证明问题. 3.能综合利用对数的相关知识解决问题. 1 预习导学 2 课堂讲义 3 当堂检测 挑战自我,点点落实 重点难点,个个击破 当堂训练,体验成功 [预习导引] 1.对数的换底公式 logcN log N 换底公式: a = (a>0,a≠1,c>0,c≠1,N>0). logca lg N ln N 最常用的换底公式是 logaN= 和 logaN= . lg a ln a 2.换底公式的两个重要推论 n (1)loga b =mlogab. m n 1 (2)logab= . logba 要点一 利用换底公式求值或化简 例1 求解下列各题: lg 2 (1)化简(log43+log83)lg 3; ?lg 3 lg 3 ?lg 2 解 方法一 原式=?lg 4+lg 8?lg 3 ? ? ? lg 3 lg 3 ? lg 2 ?· =? + ?2lg 2 3lg 2 ? lg 3 lg 3 lg 2 lg 3 lg 2 1 1 5 = · + · = + = . 2lg 2 lg 3 3lg 2 lg 3 2 3 6 方法二 原式=(log223+log233)· log32 ?1 ? 1 5 5 ? ? =? log23+ log23?· log32= log23· log32= . 2 3 6 6 ? ? (2)已知log1227=a,求log616的值. 解 方法一 由 log1227=a,得 =a, 2lg 2+lg 3 3-a ∴lg 2= lg 3. 2a 3-a 4× 4?3-a? lg 16 4lg 2 2a ∴log616= = = = . lg 6 lg 2+lg 3 3-a 3+a 1+ 2a 3lg 3 方法二 由于log1227=log1233=3log123=a, a ∴log123= . 3 3 3 于是 log312= ,即 1+2log32= . a a 3-a 因此 log32= . 2a 4 4 而 log616=4log62= = log26 1+log23 4?3-a? 4 = = = . 1 2a 3+a 1+ 1 + log32 3-a 4 4?3-a? 故 log616= . 3+a 规律方法 1.利用对数的换底公式计算化简时,通常有以下 几种思路: 一是先依照运算性质:利用对数的运算法则及性质进行部分 运算,最后再换成同一底. 二是一次性地统一换为常用对数,再化简、通分、求值. 三是将式子中的对数的底数及真数改写为幂的形式,然后 n m n 利用变形 loga b = logab. m 对出现的对数进行化简,当底数和真数都较小时,容易发现 它们之间的关系,然后再借助对数的运算法则求值. 2.对于换底公式,除了正用以外,也要注意其逆用以及变形 应用. 跟踪演练1 (1)求值:log89· log2732. lg 9 lg 32 2lg 3 5lg 2 10 解 方法一 log89· log2732= · = · = . lg 8 lg 27 3lg 2 3lg 3 9 方法二 log89· log2732=log2332· log3325 2 5 10 = log23·log32= . 3 3 9 (2)已知log23=a,log37=b,试用a,b表示log1456. log27 log27 解 ∵log23=a,∴log37= = =b. log23 a ∴log27=ab. log256 log28+log27 3+log27 3+ab ∴log1456= = = = . log214 log22+log27 1+log27 1+ab 要点二 利用对数的换底公式证明等式 2 1 2 例 2 已知 a,b,c 均为正数,3 =4 =6 ,求证: + = . a b c 证明 不妨设3a=4b=6c=m,则m>0且m≠1, a b c 于是a=log3m,b=log4m,c=log6m. 1 1 1 则由换底公式可得 =logm3, =logm4, =logm6, a b c 2 1 于是 + =2logm3+logm4=logm(32×4) a b 2 =logm36=2logm6= . 因此等式成立. c 规律方法 1.在已知条件中出现幂值相等的形式时,通常可 以设出幂值的结果,然后将指数式转化为对数式,然后结合 对数的换底公式、运算法则等进行化简和变形. 2.由于对数的运算法则都是针对同底数的对数才能成立的, 因此变换底数是解决对数式证明问题的重要环节,当出现的 1 对数的底数不同,但真数相同时,可利用性质logab= 进 logba 行变换. 跟踪演练2 已知2m=5n=10,求证:m+n=mn. 证明 由已知可得m=log210,n=log510, 1 1 因此 =lg 2, =lg 5, m n 1 1 于是 + =lg 2+lg 5=lg 10=1, m n n+m 即 =1,故 m+n=mn. mn 要点三 对数换底公式的综合应用 1 1 例 3 (1)已知 11.2 =1 000,0.011 2 =1 000,求 - 的值; a b a b 解 ∵11.2a=1 000,∴lg 11.2a=lg 1 000, 即a· lg 11.2=3, 1 1 于是 = lg 11.2. a 3 1 1 同理可得 = lg 0.011 2. b 3 1 1 1 1 于是 - = lg 11.2- lg 0.011 2 3 a b 3 1 11.2 1 1 = lg = lg 1 000= ×3=1. 3 0.011 2 3 3 (2)设logac,logbc是方程x2-3x

以下是今天幸运会员获奖名单

www.pj669.com|62284811|moregood|22261.com|7011.ag|www.mitao234.com|wwwcg998net|84299.com|78181|gaoyunchen|www.28563563.com|www.3lwl.com

vns0766com|598698com|www.nv333.com|xpj0452com|tz602.com|yezhulu最新地址2019|zzzttt视频|c147258yq|www.mgm5155.com|强制匹配都市在线玩|424169708|9516vip|8813jj. com|wwwtyc508com|www.2015la.com|3638com|m.kb836.com|www.bbs.com|ag1826cn|c2437249078|lctoo9880.com|www. 2174hu.com|www.mmm6165.com|wwwbet9999com|www.embedsys.net|3333aq.com|a18888.com|www.5168t.com|www112518com|493TV路cn|mark-6.com|www.p0907.com|bmw8842com|www.4949cf|1592long|ks6690net|www443779com|www.h8009.com|wangyijun52|402j1|WWW.123000.COM|vinmsm|www755818com|bnuawx.com|hg0335com|sshh520|5504nn|www290199com|66668hgcom|www.5zdm.com|xuyang_2321@qq.com|wwwsqshunhuicom|www.283322.com|www.0166f.com|www.x9567.com|wwwjstv345com|WWW.HG9181.COM|6ttle|666999|www677077com|wwwztknet|vns600300|308878.com|se779|www.hg0591.cc|www.8858sun.com|13661、c0m|wwwhg38848com|www2836536365com|wwwhg00525com|www.2163.bbo998.com|www.g1841.com|www.hainan4.com|liang186|wst.vip|qy8497com|www.aa894.com|www.4435.com|zxl6312|www.t3838.com|wwwlxyl50com|WWW.KJ589.COM|www.155741.com|www.229911.com|biz-nike.com|www.4fs2.com|vv466|WWW.HG4134.COM|wwwsss189com|www.957ee.com|WWW.FCW518.COM|wwwwycglcom|33aa.com|wwwMG9088COM|www.yl12388.cc|www.0072999.com|www.sbd3300.net|www888886com|wwwava88.ppcom|www.tjxcbc.com|www558kcom|WWW.MGM678.COM|ks6126.vip|www580913com|2964.com|yaoji8.com|luoqi11888|yf9222.com|www.9969r..com|www.3388777.com|www.50s8s.me|4818.com|AV基地网永久网址AⅤJD888..co|941fmnu.wc1jq6|WWW.K345678.COM|www.hg17.com|bobitong.com|www.1234.cp|www.hugefuli.com|www.sabic-pc.com|wudi|www.847se.com|wwwhg6958com|www.hhh110com.com|www368avcom|wwwhhg188com|9721.vip|7363.com|www.xpj730.com|www.ppkbet22.com|7755311com|wwwhg789bet|wwwhg8708com|www7774x,C0em|www.66500.com|www.11533.com|27619469@qq.com|www.613x.com|js6361com|jj198439|www.hg9721.com|www478eecom|www.d555888.com|wwwbet86666com|www.ww678.com|wwwzytgtfcom|www.6688018.com|www67666com|hg3841.com|www.dufang8.com|www3467jcc|www.k8k8.com|www.822599.com|wwwtyc5578com|mo7777.net|www.u1944.com|43094|www.147qqq.com|betzuqiu.com|hg1201.com|ljhbaby|www.5dh5.com|22559908.com|yb3723com|mg8921.vip|1076002|WWW,41616,com|www.f68xx.com|

77288a.com|bet365a5.com|958TV|388h.com|WWW.T345.CCK345.CC|www33311567com|ag88094|25444u.com|www77777aaacom|6992eecom|maomaomao|ben2222ss.com|www08222com|zihuo|www830762|nidaye|www.mg.hn|koko555|ccccc486|hg8224.com|1018503199|ag0325com|www.av9939.com|WWW.810654.COM|www.32126v.net|www.btt918.cn|xmm05|www.2005647.com|ky22.tv|members.vobes.com|www.145544.com|ccl33033|97178.com|yt777999.com|wwwhj8568com|wan3048.com|39800com|www.lehu129.com|wwwtk99999com|8735587|www.am339.com|535444.com|www.8677.com|881589.com|ag.szh36.com|08322004.com|www776611con|bet5375com|ET592.COM|www.pj70888.com|qq650689|wwwww48538com|www82899com|wz0222|wwwvvvcom|www.acc777.com|888ivcom|www.kpk8.com|www.500vp.com|www.uuu11.com|bbs4.1soccer.com|1679641119|185070791@qq.com|www.3538.bifa8877.com|ki.oo6.com|www.blr8826.com|lzx5|fafa141|wwwyahu195com|www114886com|wwwam22222com|4887wwcon|www.054ee|www.yl988.com|www.uf8810.com|www.at64.com|99006p|www.1481.com|wwwbgj188com|ppk222.com|fafa303|www.ben8844.com|www:9920e:com|jianjianghui|853964com|www.y2665.com|www.784567.com|ym1889.com|www.22scsc.com|www187cfcom|www.307rr.com|ag81401.com|www.099xpj.com|www579765com|mk20130325|666608com|cqw54565258|www.06646.com|www.9138.com|092333.com|hg6605com|fjn9302|www.v5f3.com|www.879.com|poweroc@gmail.com|www.kmtxd.cn|www.2078w.com|h440582|cxl118|lyd3434|wwwjs33233com|h00444.com|www.479898.COM|WWW.A6889.COM|www.098sp.com|ampj686|xiayun123|zfqui77|www.2127y.com|wwwblr905com|shenximen|123888.com|6888.qg|www.jinsha318. com|36668x. com|zunyi212.com|www.331159.com|www.s366.com|521av|www33366003com|jcrbcom|8801266,CoM|WWW.V8890.COM|822666com|www.108a1.com|www.805mm.com|www.666999.com|tangming88|zyguang|www.282ks.com|www.ke4848.com|flb0312|987dy.com|88058.com|www.1846.com|lingdj1an|www.x66159.com|g4teger|WWW.FX969.COM|15263847890|www644655com|29.comc29hh.com|alw240579|1234567|www.92966.com|2493.vip|WWW.66566.CC|gc0909|750X.COM|847000com|www.138y.com|ming558|www37123net|www.26048.com|WWW.6099.COM|jyg0755|437suncom|www.jinsha135.com|

www.985201.com|wwwr2233com|4340l|89hk.net|f2009116|bm1399.cc|pujing95.com|172903.shtml|wwwfun197com|8855xu|www525844com|32365.com|sunchuanchun|32525.com|www.265sn.com|mm888|www.008727.CC|www.cr7088.com|www.x55.net|www.seh1.com|www.xg0001.com|wwwa878cc|www.1213ooo.com|www.3085.com|www72englishcom|94vw.com|610813631|46333333.com|wwwvip050com|www.ks068.com|0003k|1000rt.com|wwwbet3169com|hw139|Gcp11. com|liyukun222|zhangqi|wwwkk3456com|lq5959|www.amhg2222.com|agks7572com|4859com|101ksnet|wwwhg7154com|26k66.com|754hn.com|www.js383vc.com|mg3104.com|www.0009yh.com|1060619852|WWW .006GYH.com|05353s.com|wwwyh7863com|www.259msc.com|www.utpbaby.com|3ajizz|845322com|www.6120.com|99bocai|WWW.HG2482.COM|www.874347.com|wwwfengyunc|www9585689com|www9618us|www.dafa222.net|5303011.com|dzj990.com|cz10611.com|ckj1949|mingshi|hg7689com|qy2731com|liuqi0|lt1151.com|49555.cc|v70999|js88656.com|m kpd109|szz222|WWW.350MSC.COM|zhangsirong|289915024@qq.com|WWW.578000.COM|bx8808.com|jinku40.com|a370733141|www638msccom|wwwwx789com|ld003.com|ag6052.com|www.7474vk.com|673388com|www.78794.com|xb3|www.969601.com|yc887b. com|zhi222|www.yy375.com|www.229333.com|www95544vnscom|te02com|gm1789com|20770808|800756com|bm2699.com|guangfudb|kkkbo最新网址入口|wwwmgm3388com|70303vv.com|wwwkaifayulechangcom|v2335com|WWW.YF02.COM|4152bet|1344013208|qy6494vip|280757133@qq.com|www5086789com|zhaisiyan|www.4444yy.com|www546456com|www9m138com|dlu2013|www.723666.com|www.2394444.com|qq353535|99hh163com|WWW.V7V7.COM|chunchun66|yumianzhi@yahoo.com.cn|uu.163.ccm|www.sgqyh.com|WWW.WWW.OFHTFTJ.COM|ag5637com|www.333955.com|www.wrbld.top|www.9940t.com|www.5KBKB|www.4444xe.com|www.hg29.net|WWW.tta30. com|www.20050.net|www.32627.com|1257996994|jmnyg520|WWW.WWW.31166.COM|411321c.rt4wf7.cn/?p=465'|www.qifa800.com|xq9595|www.848222.com|ag6066.com|www.www-4119.com|88128z.com|http://www.978lulua02.xyz|vns204com|www.3000vvco|www.1108e.com|www.sj222.com|ydll716|www.av8816.com|www04733com|mg4136.com|qifa992|ggyy77|www.r00765.com|70088121.com|wwwbet6286com|dlpc|www.9768js.com|

fvb168|hg1693com|dyx1234|18677201112|2221366net|872384i5th|w2801|18uij. com|www.62289b.com|www.yeyeqi.com|hg503311com|566509.com|dd7070.com|www.017111.com|www.3311xj.com|www.7893w98.com|635871244|www.888235.com|www.910kk.com|wwwwwwrzbysccom|www.209091.com|lv4422|www.kankansd. com|www.8888ye.con|wwwpjbet031com|agks4787com|500xx50com|www.84js.com|854190com|www.69179.com|ww.yingtao991.com|www.wd11627.com|clangligela|www.48488c.com|sea51|www.19488.com|www.savk12.com|wwwr6266com|www.avttt.com|88gg163com|578885718|897472com|dnf包管理 与yum|38wen.com|wwwpj001111com|www.6865c.com|www233123com|hanfei123|www586zzcom|ss077|zillow.com|www18066com|chenmeiping|www.8456.cc|wwwrb230com|hg0332.com|luo0920|wwwhaotingcom|www.66882.com|899358com|www.7869633.com|wwwhm0027com|www.8010728.com|www66365365com|www.v7544.com|www.yl154.com|wwww.43678.com|z00189.com|www.y36hh.com|828926com|www.kkkkk8.com|www.hg26280.com|ktv99com|www.hgbb.co|zl1010com|www234567tv|www.7000828.com|mjb158|1027qiao|45kvkb|www.hg163.com|www.1782k.com|wwwmanhadun8com|492999com|91a1新地址|www.823309.com|smy888|stm873006896|0777.bet|https://m.sogou.com/web/searc|807286com|www.698tm.com|www4444xcozm|5654vip|wqr1155@163.com|www.164101.com|www.3344tt.com|bet5332com|897404com|xpj6215com|www.yemalu.pW|cq915017210|www.rrr333.com|2226566471@163.com|2267316|www.zzz13|wwwgxjartsfest2008com|www775558com|pj700.com|www.2340898.com|long2933com|www.vns1290.com|2306h.com|wwwyli222com|699xinpujing|www.5128msc.com|39439n.com|wwwbm8549com|www.9599117.com|www.hg559q.com|www.164vns.com|www.drf0661.com|yhcy6600╭(╯R|463k8.com|www.99567v.com|WWW.15303.COM|www.1397710.com|www.999377.com|wqh362523|www.3052004.com|by1239网站|pkpk89|yf2666com|2uezcom|13670472563|681378com/|330451196@qq.com|wwwvipv1100tv|456fff备用网址|www.7506.com|cah0532|www.jnqdsy.com|www9785999com|www.dc1177.com|houhui|99cu.com|731msc.com|www.7269l.com|www778012com|DD4. APP.com|bet6077.com|www.bmw9784.com|字节跳动期权换购|pjwzzz.com|77075ggcom|www.822272.com|hg67804.com|www.988yin.com|www.kkqqq.com|www78758ccom|js8855dcom|0891xpj.com|m.hg0305.cn|www.4444abc.com|22290n.com|kphbeijing.m.chenzhongtech|www.bm5244.com|alanhe25|

以上会员名单排名不分前后