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-,*,-,2,.2.1,第,2,课时对数运算,1/27,2/27,1,.,对数运算性质,3/27,4/27,5/27,2,.,换底公式,log,a,b=,(,a,0,且,a,1;,c,0,且,c,1;,b,0),.,6/27,做一做,2,计算,:log,3,+,lg 100,-,ln 1,+,log,2,8,=,.,解析,:,原式,=,log,3,3,-,3,+,lg,10,2,-,0,+,log,2,2,3,=-,3,+,2,+,3,=,2,.,答案,:,2,思索辨析,判断以下说法是否正确,正确在后面括号内画,“,”,错误画,“,”,.,(1)(,-,2),3,=-,8,可化成,log,(,-,2),(,-,8),=,3,.,(,),(2)log,3,(,-,4),(,-,5),=,log,3,(,-,4),+,log,3,(,-,5),.,(,),(3)log,2,(,-,3),2,=,2log,2,(,-,3),.,(,),(4)lg 2,+,lg 5,=,1,.,(,),(5)log,4,8,=,log,2,3,.,(,),答案,:,(1),(2),(3),(4),(5),7/27,探究一,探究二,探究三,思维辨析,探究,一,对数运算性质应用,8/27,探究一,探究二,探究三,思维辨析,9/27,探究一,探究二,探究三,思维辨析,10/27,探究一,探究二,探究三,思维辨析,探究,二,换底公式应用,11/27,探究一,探究二,探究三,思维辨析,12/27,探究一,探究二,探究三,思维辨析,13/27,探究一,探究二,探究三,思维辨析,【例,3,】,已知,log,18,9,=a,18,b,=,5,求,log,36,45,.,(,用,a,b,表示,),分析,:,先利用指数式和对数式互化公式,将,18,b,=,5,化成,log,18,5,=b,再利用换底公式,将,log,36,45,化成以,18,为底对数,最终进行对数运算,.,14/27,探究一,探究二,探究三,思维辨析,15/27,探究一,探究二,探究三,思维辨析,探究,三,对数综合应用,16/27,探究一,探究二,探究三,思维辨析,17/27,探究一,探究二,探究三,思维辨析,18/27,探究一,探究二,探究三,思维辨析,19/27,探究一,探究二,探究三,思维辨析,因忽略对数真数为正而致错,典例,解方程,lg(,x+,1),+,lg,x=,lg 6,.,错,解,:,lg(,x+,1),+,lg,x=,lg,x,(,x+,1),=,lg(,x,2,+x,),lg(,x,2,+x,),=,lg,6,x,2,+x=,6,解得,x=,2,或,x=-,3,.,错因分析,:,错解中,去掉对数符号后方程,x,2,+x=,6,与原方程不等价,产生了增根,其原因是在,x,2,+x=,6,中,x,R,而在原方程中,应有,再验根即可,.,正,解,:,lg(,x+,1),+,lg,x=,lg,x,(,x+,1),=,lg,6,x,(,x+,1),=,6,解得,x=,2,或,x=-,3,经检验,x=-,3,不符合题意,x=,2,.,20/27,探究一,探究二,探究三,思维辨析,21/27,探究一,探究二,探究三,思维辨析,变式训练,方程,log,3,(,x,2,-,10),=,1,+,log,3,x,解是,.,解析,:,原方程可化为,log,3,(,x,2,-,10),=,log,3,3,x.,所以,x,2,-,10,=,3,x,解得,x=-,2,或,x=,5,.,检验知,方程解为,x=,5,.,答案,:,x=,5,22/27,1 2 3 4 5,1,.,lg 2,+,lg 50,=,(,),A.lg 52B.lg 25C.2D.lg 48,解析,:,lg,2,+,lg,50,=,lg(2,50),=,lg,100,=,2,.,答案,:,C,23/27,1 2 3 4 5,24/27,1 2 3 4 5,25/27,1 2 3 4 5,4,.,已知,3,a,=,2,用,a,表示,log,3,4,-,log,3,6,=,.,解析,:,3,a,=,2,a=,log,3,2,log,3,4,-,log,3,6,=,log,3,2,2,-,log,3,(2,3),=,2log,3,2-log,3,2-log,3,3,=a-,1,.,答案,:,a-,1,26/27,1 2 3 4 5,5,.,计算,:(1)3log,7,2,-,log,7,9,+,2log,7,;,(2)(lg 2),2,+,lg 2lg 500,+,lg 125,.,解,:,(1),原式,=,log,7,8,-,log,7,9,+,log,7,=,log,7,8,-,log,7,9,+,log,7,9,-,log,7,8,=,0,.,(2),原式,=,lg,2(lg,2,+,lg,500),+,3lg,5,=,lg,2lg,1,000,+,3lg,5,=,3lg,2,+,3lg,5,=,3(lg,2,+,lg,5),=,3lg,10,=,3,.,27/27,
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