山东省武城县第二中学高中数学《3.2.1对数及其运算》第3课时导学案(无答案)新人教B版必修1

3.2.1 【预习学案】 换底公式与自然对数 1. 对数及其运算(第 3 课时) loga N = loga b . 2. 3.利用换底公式证明: 叫自然对数. logb a ? 1 loga b 4.利用换底公式证明: log a m b n ? n log a b . m 强化训练: 1.求值. ① ln e ; ②e ln ? 2 ; 1 ③ ln 5 ; ④ ln 21 . 2.计算 ① log5 4 ? log8 5 ② log 2 1 1 1 ? log 3 ? log 5 25 8 9 ③ log2 3 ? log27 125 ④ lg 1 5 ? lg ? lg 12.5 ? log 8 9 ? log 27 8 2 8 3.计算下列各式的值 ① log4 8 ? log1 3 ? log 9 2 4 ② (log 2 5 ? log 4 )(log 5 2 ? log 25 1 5 1 ) 2 2 4.求解下列各题. (1)已知 2 logx 25 ? 3 log25 x ? 1 ,求 x . (2)已知 log9 5 ? a , log9 7 ? b ,求 log35 9 . (3)设 3 ? 4 ? 6 ? 1,求证 x y z 1 1 1 ? ? . z x 2y 3 3. 2.1 对数及其运算(第 3 课时) 【限时训练】 1. log5 2 ? log4 25 等于( ) A.-1 2.化简 log1 b ? loga a B. 1 2 C.1 D.2 1 的值为( ) b B.1 x ?x A.0 C. 2 loga b 的值为( ) C.2 D.-2 loga b 3.若 x log3 4 ? 1 ,则 4 ? 4 A. 8 3 B. 10 3 D.1 1 ? log 3 6 ? log 6 x ? 2 ,则 x =( ) 3 1 A.9 B. C.25 9 1 1 a b 5.设 2 ? 5 ? m ,且 ? ? 2 ,则 m =( ) a b 4.若 log 5 A. 10 6. e ln 3 D. 1 25 B.10 C.20 D.100 ? e ? ln 2 等于( ) B.2 C. A.1 5 2 . D.3 7.计算 log4 3 ? log9 8 = 8.已知 f (3x ) ? 2x ? log2 3 ,则 f (21005 ) 的值等于 . 9.若 log 3 7 ? log 2 9 ? log 49 m ? log 4 1 ,求 m 的值. 2 10.已知 log9 8 ? p, log27 25 ? q ,试用 p、q 表示 log5 2 . 4

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