ĐỀ THI THỬ ĐẠI HỌC NĂM HỌC 2012-2013 MÔN TOÁN ĐỀ 28 docx

*        4 21 2 1 log 2 log 4 18 0 2 xx      : -2 < x  18 Ta      4 21 2 1 log 2 log 4 18 0 2 xx     <=> 24x   4 18 x ( 1 )  4 18 x => 2 + x = 20  t 4 , 0  t < 4 20        4 4 4 2 42 4 4 4 4 4 4 32 0 20 0 20 0 20 8 4 0 20 4 20 4 0 20 2 20 2 18 20 2 2 5 2 0 16 18 20 2 2 t t t t t t tt tt t tx t t t t xx                                                   <=> -2 < x  2 2: : 2 4 1 log 4 3xx <   4 1 log 3x   2 2 4 3 0 3 4 3 1 4 30 22 31 xx x xx x x x x                         2 4 4 11 log 3 log 4 3 x xx    > 0 <=>     2 44 2 44 log 4 3 log 3 log 4 3.log 3 x x x x x x        > 0 ( 1 ) log 4 2 43xx > 0 <=> x < 2 - 2 V x > 2 + 2 log 4 ( x  3 ) > 0 <=> x > 4 *  TH 1: x > 4, bpt ( 1 ) <=> log 4 2 43xx > log 4 ( x  3 ) <=> 2 43xx > x  3 <=> x 2  4x + 3 > ( x  3 ) 2  x > 4 TH 2: 2 + 2 < x < 4, log 4 2 43xx > 0log 4 ( x  3 ) < 0 => bpt TH 3: 3 < x < 2 + 2 , bpt ( 1 ) <=> log 4 2 43xx > log 4 ( x  3 ) <=> 2 43xx > ( x  3 ) <=> x 2  4x + 3 > ( x  3 ) 2  ( 3; 2 + 2 )  + 2 ) ( 4; +  )      22 1 5 3 1 35 log log 1 log log 1x x x x           22 1 5 3 1 35 log log 1 log log 1x x x x     <=>                     22 3 1 3 5 5 22 3 1 5 5 1 2 2 2 2 55 2 5 22 5 2 5 2 2 log log 1 log log 1 0 log log 1 .log 1 0 log 1 .log 1 1 : 1 1 log 1 1 log 1 1 log 1 0 15 11 x x x x x x x x x x x x do x x x x xx xx xx xx xx                                                          2 22 2 22 50 12 15 1 (5 ) 5 10 1 1 1 0 10 01 1 (1 ) x x x x xx x x x x x x x xx                                        12 5 )    2 1 1 3 3 11 log 1 log 2 3 1 x xx    ( 1 )   2 2 10 1 2 3 1 0 0 2 2 3 1 1 3 1 10 2 11 3 2 x xx x xx x x x x                                       2 2 1 2 3 1 3 1 0 2 3 1 0 2 log 2 3 1 0 3 2 3 1 1 1 2 10 log 1 0 1 0 11 x xx xx xx x x xx x                                       Ta TH 1: -1 < x < 0 TH 2: 0 < x < 1 2 V 1 < x < 3 2   TH 3: x > 3 2        2 11 2 33 11 2 33 11 33 2 log 1 log 2 3 1 0 log 1 log 2 3 1 0 log 1 .log 2 3 1 1 2 3 1 x x x x x x x x x x x x                    <=> x 2 - 3 2 ta     13 ) (1; ) 5; 22        23 34 2 log 1 log 1 0 56 xx xx        2 1 0 1 5 6 0 6 xx x x x                                  3 3 33 3 3 3 3 log 1 2log 1 3. log 1 (2log 4 3) log 4 00 1 6 1 6 .log 4 log 1 0 : 1 0;2log 4 3 0 6 x x x x x x x x do x x                   x  6 > 0 <=> x > 6; log 3  * -1 < x < 0 =>  3   3   3    2 4 2 1 log 22 x x x        ( 1 )   1 2 1 2 x x x            TH 1:   2, bpt ( 1 ) <=> 42 4 2 2 2 x x x x x x        2 2 4 2 ( 2) 6 2 0 22 2 3 7 4 2 (2 ) 12 2 2 0 12 12 x x x x x xx x x x x x xx x x                                                  TH 2: 1 2 < x 2 42 4 2 2 4 2 (2 ) 2 1 2 2 0 1 3 2 x x x x x x x x x x x x                          1 ; 1 3 1;2 2;3 7 2 S         2 2 2 log 4 5 4 x x       2 2 2 log 4 5 4 x x      2 11 22 2 11 22 22 2 log 4 0 3 log 2 4 8(1) 44 4 2 2 1 2 1 log 9 2 log 3 (2) 4 4 8 4 4 xx x xx x x x x x x x                                     Bpt ( 1 ) 2 32 10 8 0 0 8 16 44 2 6 16 35 4 0 0 44 xx xx x xx xx                           Bpt ( 2 )     94 21 0 0 4. 4 44 44 2 1 17 4 17 9 00 4 8 8 4 x x x x x xx xx                            4 4 8 16 ;; 17 9 3 5                2 2 2 2 2 4 log log 3 5. log 3x x x     2 x ( t  3 ),                  2 2 2 2 2 2 3 5 3 30 30 3 . 1 0 2 3 0 10 30 30 1 5 3 2 3 5 3 3 . 1 5 3 1 34 t t t t t tt tt t t t tt t t t t t t t t                                                                   V 1,t   2 1 log 1 0 2 xx      2 x <4 <=> 8 < x < 16    1 8;16 2       2 2 log 2 log 10 22 0 x xx   ( 1 )   2 2 53 10 22 0 2 5 3 53 0 log 1 53 2 12 2 x xx x x x x x                               ( * )  TH 1: 2 < x < 5 - 22 5 3 5 3 3 1 0 log log 1 2 2 2 2 xx        Bpt ( 1 ) <=> x 2 -10x + 22< 1 <=> x 2  : 2 < x < 5 - 3 TH 2: x > 5 + 3 => 2 log 1 2 x  Bpt ( 1 ) <=> x 2 -10x + 22 > 1 <=> x 2 -10x + 21 > 0 <=> x < 3 V x > 7  - 3 V x > 7      2 2 1 log 6 4 * x xx       2 0 1 1 1 6 0 0, 2 xx x x x x               x 2 + x  6 > 0 <=> x < -3 V x > 2  TH 1: - 1 < x < 0 => x 2 + x  )<=>- (x 2 + x  6)  ( x +1) 2 <=> 2x 2 + 3x  5  0 <=> x  - 5 2 V x  1 (VN ) TH 2: 0 < x <2 => x 2 - (x 2 + x  6)  ( x +1) 2 <=> 2x 2 + 3x  5  0 <=> - 5 2  x  1 => 0 < x  1 TH 3: x > 2, bpt (*)<=> x 2 + x  6  ( x +1) 2 <=> x  - 7 ( VN )   1  2 4 5 1 log 22 x x x    HD:  5 4  x  2 N  5  5 4 < x <2 => 61  x < 2  61  x < 2 V 2 < x  5      2 2 22 1 log 2 1 log 2 0 2 x x x    ( 1 )   2 2 1 0 0 2 0 2 xx x x x              Bpt ( 1 ) <=> 2 2 1 2x x x   ( 2 )  TH 1: x < 0, bpt ( 2 ) <=> - ( 2x  1 )  x 2  2x <=> -1  x < 0 TH 2: x > 2, bpt ( 2 ) <=> 2x  1  x 2  2x <=> x 2  4x + 1  0 <=> 2 < x  2 + 3 -1  x < 0 V 2 < x  2 + 3  5x +   2 3 4 2 2 22 6 .log log 5 5 6x x x x x x x x x        ( 1 )  x 2  0 => 0 < x  3            2 2 2 2 2 2 6 log 5 log 5 log 5 0 log 5 ( 6 1) 0 2 x x x x x x x x x x x x x x                  22 2 2 2 6 1 0 6 1 01 01 01 13 13 5 1 2 3 5 0 2 61 x x x x x x x x x x x x xx x x x                                                   2 x  0 => x log 2 x  0 => x log 2 x  5 < 0 => bpt ( 2 )    3 => 0 < log 2 x  log 2 3 1 < x  3 => x.log 2 x  3. log 2 3 => x.log 2 x - 5  log 2  2 13 6 1 0 x x x x            <=> 5 2 < x  3  5 2 < x  3    2 3 1 1 33 1 log 5 6 log 2 log 3 2 x x x x      HD:: ( x  2 ) ( x  3 ) > 2 3 x x   <=> x 2  9 > 1  10