Bài tập về hàm số mũ và logarit

Hocmai.vn – Website h c tr c n s t i Vi t Nam Khóa h c: Pen C – N3 (Th y Lê Anh Tu n – Th y Nguy n Thanh Tùng) Chuyên đ : Hàm s m - Logarit HÀM S MŨ HÀM S LOGARIT ĐÁP ÁN BÀI T P T LUY N Giáo viên: LÊ ANH TU N n gi n bi u th c sau: Bài A H a  n  b n a  n  b n  ab  0;a   b  a  n  b n a  n  b n B  a 1  x1 a 1  x 1  xa 1  ax-1  1  1 1  1 a x  a x   ng d n gi i a  n  b n a  n  b n A  n   a  b n a  n  b n   a 1  x1 a 1  x 1  B  xa 1  ax-1  1  1 1   1 a x  a x        a n  bn  bn  a n a n  bn bn  a n   n n n n a n  bn bn  a n n n  b a  n na b  a b  n n  a b  n n   a b   a b      4a n bn b2n  a 2n 2  x2  a   x  a x  a  x  a x2  a        ax   x  a x  a  ax ax Bài Rút g n bi u th c sau: 1 1  8b  a  a b a  2b  B 1        13 3 3    2a b 4a 2a b b  1  b 3   A a     a  a  ab  4b  a  8a b H ng d n gi i 3 1 2  a  a  8b  a  8a b b a3 3     A a a    1 1  a  a  ab  4b  a  2a b  4b a  2b 1 2 a  a  8b   3 3 3 3 a  a  2a b  4a b  2a b  4a b  8b  8b  a  a b a  2b B  1 1        3 3 3 2a b 4a 2a b b     3 3 a  a  8b  a  8b  a3    13  23 23  2   a  2b  a b     8b  a  a b      1      2b  a  4b  2a b  a          1   31   3 3  4b  2a b  a   a  2b      2 8b  a  6ab  8b  a    a b3        ab 3   8b  a   13   13    2b    a          n gi n bi u th c: Bài a a2 a 2  b2 b Hocmai – Ngôi tr 3  1 ng chung c a h c trò Vi t !! a b   a2 a4 T ng đài t v n: 1900 69-33 3 a a  a3  - Trang | -      Hocmai.vn – Website h c tr c n s t i Vi t Nam Khóa h c: Pen C – N3 (Th y Lê Anh Tu n – Th y Nguy n Thanh Tùng) a c b a a b ng d n gi i H a 5 a2 a a b  b2   1 a b 2 a a c a 5 b a b a a b b b a  a3 d 3 a b b  1  a  3  a   b    a 3 b 3 3 b    5 7  b  a  a b  b   a 5 a b b    log9   25log125  49log7 a  814     1    ab    2a     a a   b  2 b 1 3  1  d a  b   ab   a   b2   2a  b  4a  b    Bài Tính giá tr c a bi u th c sau:   a a  b    a  1a  1 a a   a   a  a  a  1 a   a  a 7 a 1  Chuyên đ : Hàm s m - Logarit  b   a   b b 161log4  log 33 log 5  log7 9log7  log  5 c 72  49    H ng d n gi i   log9   4  log  log 23   25log125  49log7       53  log7 a  814      log  log 3    31log3       19  4    1log b 16 4 log 33 log 5 2 1log     2log2 36 log5  16.25  3.26  592  log7 9log7 1   log  log 92 log7 5  52 log5  72     18  4,5  22,5 c 72  49   72 7  36 16    Bài Tính giá tr c a bi u th c sau: a A  log9 15  log9 18  log9 10 b B  2log  log 400  3log 45 3   d D  log  log 4.log  c C  log 36  log H ng d n gi i a A  log 15  log 18  log 10  log 15.18  log 33  log 33  10 2  36.45  b B  2log  log 400  3log 45  log    log   log 3  4 20  3 3 Hocmai – Ngôi tr ng chung c a h c trò Vi t !! T ng đài t v n: 1900 69-33 - Trang | - Hocmai.vn – Website h c tr c n s t i Vi t Nam Khóa h c: Pen C – N3 (Th y Lê Anh Tu n – Th y Nguy n Thanh Tùng) Chuyên đ : Hàm s m - Logarit 1 1 c C  log 36  log  log  log  log 2.3  2 2 1 d D  log  log 4.log    log  log 3.log    log  log    log 2   2 Bài Tính giá tr bi u th c sau:    A  log  2sin   log cos 12  12  B  log    3  log  49  21   D Tìm x bi t: log x  log 216  2log 10  4log 3 C  log10 tan  log10 cot H ng d n gi i         A  log  2sin   log cos  log  2sin cos   log sin   log  1 12  12 12 12  6    B  log    3  log    49  21   log   733  C  log10 tan  log10 cot  log  tan 4.cot   log1   49  21    log 7     D Ta có 1 6.34 35 log x  log 216  2log 10  4log  log  log 10  log 34  log  x  3 50 10 Bài Rút g n bi u th c: A   loga b  log b a   loga b  logab b  log b a  B  log 2x2   log x  x log x  log x1   log 22 x C  loga p  log p a  loga p  log ap p H  log a p ng d n gi i  log a b   A   log a b  log b a   log a b  log ab b  log b a     1  log ab a    log a b   log a b     log a b   log a a             log a b   log a ab   log a b  log a b  1  1   log b a log a b log a b B  log 2x   log x  x log x  log x1    log a b            log a b   log a b   log a b       log a b  1  log 22 x   log x   log x  log x  1   log x  2   3log x   log x    log x    log x   3log x   C  log a p  log p a  log a p  log ap p  log   log a p  p  1  log a2 p    log a p  log a p log a p   log a p   log p  1  log a p   log a p   log a p   log a p  log a p  a a Hocmai – Ngôi tr ng chung c a h c trò Vi t !! T ng đài t v n: 1900 69-33 - Trang | - Hocmai.vn – Website h c tr c n s t i Vi t Nam Khóa h c: Pen C – N3 (Th y Lê Anh Tu n – Th y Nguy n Thanh Tùng) Chuyên đ : Hàm s m - Logarit Bài Tính đ o hàm c a hàm s sau:   b y   sinx-cosx  e2x a y  x2  2x  e x   e y  d y  ln x2  H ng d n gi i   c y  f y  1  ln x  ln x ln x x  ex  ex ex  ex    a y  x2  2x  ex  y'   2x   e x  x2  2x  e x  x2 e x b y   sinx-cosx  e2x  y'   cosx+sinx  e 2x   sinx-cosx  e 2x   3sin x  cosx  e2x       ex  ex ex  ex  ex  ex ex  e x ex  ex  c y  x  x  y'  e e ex  ex ex  ex   d y  ln x2   y'  e y      2x x 1   ln x ln x 1  y'   x  ln x   x x x x2  ln x  ln x  2ln x   x x x Bài Tính đ o hàm hàm s sau: f y  1  ln x  ln x  y'  a y  x2 ln  x2     x4 d y  log   x4 H  b log x2  x  c y  ln x  x2   e y  log    x5   1 x  f y  log    x    ng d n gi i a y  x2 ln   x2   y'  2x.ln   b y  log x  x   y'  x   x2    x2 x  x2   2x.ln   x2    x3  x2  2x    x  ln 2    c y  ln x  y'   ln x   '   ln x   x 3x ln x    x4  x   d y  log     y' :  ln   x   x   x  ln x4      x2    2x  x    x  x   x  10x  e y  log  :    y'  ln  x    x   x  ln  x5   x  5          x 1  1 x   x 1 1 x  y' :    f y  log    x  ln10  16x x x  8x ln10  x     Hocmai – Ngôi tr ng chung c a h c trò Vi t !!    T ng đài t v n: 1900 69-33 - Trang | - Hocmai.vn – Website h c tr c n s t i Vi t Nam Khóa h c: Pen C – N3 (Th y Lê Anh Tu n – Th y Nguy n Thanh Tùng) Bài 10 Tìm gi i h n sau: ln  3x  1  ln  2x  1 a lim x0 x b lim x0 e 5x3  e d lim x0 2x e lim x0 Chuyên đ : Hàm s m - Logarit ln  3x  1 c lim ln  4x  1 x0 sin 2x ex  f lim x 1 1  x ln  x x0  2x H ng d n gi i ln  3x  1  ln  2x  1 ln  3x  1 ln  2x  1 a lim  lim  lim  32  x0 x0 x0 x x x ln  3x  1 3x ln  3x  1 3x b lim  lim  x0 x  sin 2x sin 2x 2x 2x ln  4x  1 ln  4x  1 c lim  lim 4 x0 x0 x 4x   e 5x  e 5x3  e 5e 3  lim e  d lim x0 x0 2x 2  5x  e lim x0 ex  x 1 1  lim x0 ex  x   x    1.2  Bài 11 Tìm gi i h n sau: ln  2x  1 a lim x0 tan x c lim x0 H x0 b lim x0 x0 ln  2x  1 tan x  lim x0 e 2x  e 3x 5x   d lim  xe x  x  x   e 3x  x ng d n gi i a lim b lim 2x ln  2x  1 2x tan x x x 2 Giáo viên : Lê Anh Tu n Ngu n : Hocmai.vn e 2x  e 3x e 2x  e 3x   lim  lim    x0 x0 5x 5  3x  5 2x e3x  e 3x   lim 3 c lim x0 x0 x 3x    ex    x1   x1  d lim  xe  x   lim x  e    lim  1 x x x         x  Hocmai – Ngôi tr ng chung c a h c trò Vi t !! T ng đài t v n: 1900 69-33 - Trang | -