Bài tập pt, bpt, hpt mũ và logarit chọn lọc.

Tài liệu ôn thi ñại học năm 2011 - 2012 ðỗ Ngọc Nam_THPT Trung Giã. Phone: 0949088998. Mail: Moonflower35@gmail.com. 1 BÀI TẬP PHƯƠNG TRÌNH, BẤT PHƯƠNG TRÌNH, HỆ PHƯƠNG TRÌNH MŨ VÀ LOGARIT Bài 1. ðưa về cùng cơ số ( ) ( ) 2 2 2 log 3 log 3 8 1 0 x x − − + + = . ( ) ( ) 2 1 1 1 3 10 6 4.10 5 10 6 x x x x x + + − − − + = − . 2 log 16 log 7 2 x x − = . 2 3 4 20 log log log log x x x x + + = . ( ) ( ) ( ) 1log2 2log 1 13log 2 3x 2 ++=+− + xx . ( ) 2 2 9 3 3 1 1 log 5 6 log log 3 2 2 x x x x − − + = + − . ( ) ( ) ( ) 8 4 2 2 1 1 log 3 log 1 log 4 2 4 x x x + + − = . ( ) ( ) 2 2 2 2 2 log 3 2 log 7 12 3 log 3 x x x x+ + + + + = + . 54 4 2 log 2 2 1 ≤−       − x x ( ) ( ) 2 2 1 5 3 1 3 5 log log 1 log log 1 x x x x + + > + − ( ) ( ) 2 2 4 4 4 log 1 log 1 log 2 x x x − − − = − ( ) ( ) 2 3 4 8 2 log 1 2 log 4 log 4 x x x + + = − + + ( ) + = + log 6.5 25.20 log 25 x x x ( ) 2 2 2 log log x x − = 2 0,5 31 log log 2 2 16 x         − ≤           ( ) 2 log log 4 6 1 x x   − ≤     3 2 3 log 1 1 x x − < − ( ) ( ) ( ) 3 9 27 2log 1 2log 4 1 3log 10 7 1 x x x + + + − + > ( ) ( ) 2 2 1 1 2 2 1 log 2 5 log 2 4 3 2 2 x x x x + + ≥ + + − xxxx 5353 logloglog.log += ( ) ( ) 2 2 log 2 4 3 log 2 12 x x x+ = − + + ( ) ( ) ( ) 2 3 3 9 3 log 1 2log 2 log 1 6 9 log 4 x x x x x + + + = − + + − ( ) ( ) 31log1log2 2 32 2 32 =−++++ −+ xxxx ( ) 4 2 2 1 1 1 log 1 log 2 log 4 2 x x x + − + = + + ( ) 2 4 log log 3 2 x x − − > ( ) ( ) 2 2 2 1 log log 2 log 6 x x x + + + > − ( ) ( ) 9 1 3 2log 9 9 log 28 2.3 x x x+ ≥ − − 2 3 3 1 5 6 2 .3 x x x + + + = 2 5 25 log ( 4 13 5) log (3 1) 0 x x x − + − − + > 2 2 2 3 4 2 4 2 2 16 2 4 3 log 1 log ( 1) log 1 log ( 1) 2 x x x x x x x x + + + − + = + + + − + ( ) ( ) ( ) 2 3 3 9 3 log 1 2log 2 log 1 6 9 log 4 x x x x x + + + = − + + − . ( ) ( ) 2 2 2 5 2 2 5 log 2 11 log 2 12 x x x x + + − − = − − . Đ/s : 2 2 5; 2 5 + − Bài 2. Logarit hóa, mũ hóa. 4 1 3 2 2 1 5 7 x x + +     =         2 5 .3 1 x x = 2 1 1 5 .2 50 x x x − + = 3 2 2 3 x x = ( ) ( ) 2 3 5 7 log log log log x x ≤ 2 2x 3 x 2 x 3 .4 18 − − = Bài 3. ðặt ẩn phụ − − + − + − + = 2 1 1 1 5.3 7.3 1 6.3 9 16 x x x x 16 64 log 2.log 2 log 2 x x x = 2 5 5 5 log log 1 x x x + = Tài liệu ôn thi ñại học năm 2011 - 2012 ðỗ Ngọc Nam_THPT Trung Giã. Phone: 0949088998. Mail: Moonflower35@gmail.com. 2 ( ) ( ) 3 2 5 1 5 1 2 0 x x x + − + + − = ( ) − − < − 2 2 2 2 2 4 log log 3 5 log 3 x x x 2.27 18 4.12 3.8 x x x x + = + 2 3 3 3 1 9 27 81 3 x x x x − +   =     ( ) ( ) ( ) 26 15 3 2 7 4 3 2 2 3 1 x x x + + + − − = 3 3 1 8 1 2 6 2 1 2 2 x x x x−     − − − =         2 2 2 log .log (4 ) 12 x x x = 8 2 4 16 log 4 log log 2 log 8 x x x x = ( ) ( ) 1 2 2 log 4 4 .log 4 1 3 x x+ + + < ( ) 2 25 log 125 .log 1 x x x = 2 2 5 1 5 4 12.2 8 0 x x x x− − − − − − + = ( ) 3 9 3 4 2 log log 3 1 1 log x x x − − > − 2 2 2 1 3 log (4 4 1) log (2 7 3) 5 x x x x x x + + + + + + + = ( ) ( ) 7 3 5 7 3 5 14.2 x x x + + − = 3 log 3 .log 1 0 x x x + ≥ ( ) 2 4 2 1 2 log x 1 log x log 0 4 + + = 2006 1 2 2 2 9 10.3 1 0 x x x x+ − + − − + = ðH-B-07 Giải phương trình: ( ) ( ) 2 1 2 1 2 2 0 x x − + + − = ðH-D-07 Giải phương trình: 2 2 1 log (4 15.2 27) log 0 4.2 3 x x x + + + = − A-2006 Giải phương trình 3.8 4.12 18 2.27 0 x x x x + − − = 2 2 1 3 log log 2 2 2. 2 x x x ≥ 1 1 15.2 1 2 1 2 x x x + + + ≥ − + D-2003 Giải PT: 2 2 2 2 2 3 x x x x − + − − = 2 2 3 27 16log 3log 0 x x x x − > ( ) ( ) 2 1 2 1 1 2 2 log 4 4 log 2 3.2 . x x+ + < − 4 2 2. log 2 log 16 7 0 x x+ − = ( ) ( ) 2 2 2 log 4 log 2 5 x x − > 1 2 1 5 log 1 logx x + > − + 2 ln 1 ln ln 2 4 6 2.3 0 x x x+ + − − = 2 2 1 2 2 log 4 log 8 8 x x + < ( ) 2 4 2 log 2 2 6log 1 2 0 x x + − + + = 2 10 3 2 5 1 3 2 5 4.5 5 x x x x − − − − + − − < ( ) 3 log 2 log 2 x x x x ≤ 2 1 4 2 log log 2 0 x x + − > 2 2 2 2 log 2 log 6 log 4 4 2.3 x x x − = 2 2 log 2 2 x x ≤ 2 4 0,5 2 16 log 4log 4 log x x x + ≤ − ( ) ( ) ( ) 2 2 3 2 2 2 3 2 3 2 1 log log 4 1 log log 4 2log log 2 x x x x x x x x + − = + + ðH-B-2006 Giải BPT ( ) ( ) x x 2 5 5 5 log 4 144 4log 2 1 log 2 1 − + − < + + Bài 4. Tính ñơn ñiệu của hàm số ( ) 2 3 log log 2 x x = + ( ) 2 2 2 log 1 log 6 2 x x x x + − = − ( ) 25 2 3 5 2 7 0 x x x x − − + − = ( ) 2 3 2 .3 3 12 7 8 19 12 x x x x x x x + − = − + − + ( ) ( ) ( ) ( ) 2 3 3 3 log 2 4 2 log 2 16 x x x x + + + + + = ( ) ( ) 2 log 6 4 log 2 x x x x + − − = + + ( ) ( ) ( ) ( ) 2 3 4 2 log 3 log 2 15 1 x x x x   − − + − = +   ( ) 5 7 log log 2 x x = + Tài liệu ôn thi ñại học năm 2011 - 2012 ðỗ Ngọc Nam_THPT Trung Giã. Phone: 0949088998. Mail: Moonflower35@gmail.com. 3 ( ) 2 2 3 3 log 1 log 2 x x x x x + + − = − ( ) 2 7 2 log 1 log x x x + + ≥ ( ) 2 3 log 1 log x x + > 2 2 4 2 4 log log log 64 3.2 3. 4 x x x x = + + 2 log 2 3 1 x x = − )324(log)18(log39 33 +=+− xx xx ( ) 1 2ln 1 x e x x + = + + 3 3 log 1 log 4.15 5 0 x x x + + − = . Đ/s : x = 1. ( ) 2 2 2 1 2 6 1 log 2 1 x x x x + − + = − ( ) 2 2 3log 2 9log 2 x x x − > − ( ) ( ) 5 4 log 3 3 1 log 3 1 x x + + = + 2 3 3 (2 1)log (4 9)log 14 0 x x x x + − + + = ( ) 1 2 2 4 2 log 1 1 x x x x x + − = + + − − . ñặt t = ( ) 2 log 1 x + , tính ñơn ñiệu Bài 5. Hệ phương trình 2 2 ln(1 ) ln(1 ) 12 20 0. x y x y x xy y + − + = −   − + =  ðH-B-2005 Giải hệ x y log ( x ) log y . 2 3 9 3 1 2 1 3 9 3  − + − =   − =   2 3 1 2 3 3 1 1 2 2 3.2 x y y x x xy x + − +  + + = +   + =   ðH-A-2004 Giải HPT: log (y x) log y x y 1 4 4 2 2 1 1 25  − − =    + =       −=− +=+ −+ .yx xyyx xyx 1 22 22 . ð/s: (1;0);(-1;-1) 4 2 4 3 0 log log 0 x y x y  − + =   − =   . ð/s: (1;1),(9;3) ( ) 2 2 2 4 2 0 2log 2 log 0 x x y x y   − + + =    − − =   . ð/s: (3;1) 2 2 2 2 2 log 2 .log 5 4 log 5 x x x y y y   + + =    + =   ( ) 4 4 4 4 3 8 6 x y x y x y x y − −   + =     + =    2 2 2 2 2 2 1 2 2 2 4 2 4 4 2 3.2 112 x x y y y x y − + − + +  − + =   + =   3 3 log ( ) log ( ) 2 2 4 4 4 4 2 2 1 log (4 4 ) log log ( 3 ) 2 xy xy x y x x y  − =   + = + + +   2 3 3 1 4 2 1 log 1 log 3 (1 log )(1 2 ) 2 x x y x y y  − + − =    − + =  2 2 ln 2ln 6 ln 2 ln 6 ln ln 3 2 5 x y x x x x x y  + + − + + = −   + =   2 2 2 3 3 3 3 27 9 ( , ) log ( 1) log ( 1) 1 x y x y x y x y x y + + + +  + = + ∈  + + + =  ℝ 2 1 2 1 2 2 3 1 2 2 3 1 y x x x x y y y − −   + − + = +     + − + = +    ( ) 2 2 1 2 2 2 3 2 2 2 2 2 4 1 0 x y x xy x y x x y x −     + + =      + − − + =   2 2 4 2 1 log 2log2 log 1 2 2 x y y y x   + = + +          − = +           ( ) 1 7 6 5log 6 5 1 x x − = − + 2 3 1 2 3 3 1 1 2 2 3.2 x y y x x xy x + − +  + + = +   + =   ( ) 2 log 2 8 6 8 2 .3 2.3 x x y x y y x +  − + =   + =   Tài liệu ôn thi ñại học năm 2011 - 2012 ðỗ Ngọc Nam_THPT Trung Giã. Phone: 0949088998. Mail: Moonflower35@gmail.com. 4 { ( ) 3 2 log 3 2 12 .3 81 x x y y y y + = − + = ( ) 2 log 2 2 1 2 9.2 4.3 2 .3 36 x x y x y y xy  − − =   + = +   ( ) ( ) 3 3 27 log 2 1 log 3 2 x x + − = − 2 8 2 2 2 2 log 3log ( 2) 1 3 x y x y x y x y  + = − +   + + − − =   ( ) ( ) 2 2 2 2 3 2 2010 2009 2010 3log 2 6 2log 2 1 y x x y x y x y −  + =  +   + + = + + +  )12(log1)13(log2 3 5 5 +=+− xx ( ) ( ) ln ln ln ln ln ln 1 2 3.4 4.2 x y x y x y e e y x xy +  − = − +   − =   ðH-D-2006 CM với mỗi a>0 hệ sau có nghiệm duy nhất ln(1 ) ln(1 ) x y e e x y y x a  − = + − +  − =  Chứng minh rằng hệ: 2 2 2009 1 2009 1 x y y e y x e x    = −   −      = −    −   có ñúng 2 nghiệm x > 0; y > 0. ( ) 2 2 2 2 2 2 2 4 9.3 4 9 .7 4 4 4 4 2 2 4 x y x y y x x x y x − − − +   + = +      + = + − +   . ð/s: (1; -1/2) pt thứ nhất thoát bằng hàm số. Bài 6. Tích − + + + + + + = + 2 2 2 3 2 6 5 2 3 7 4 4 4 1 x x x x x x ( ) ( ) 5 3 3 log 2 log 2log 2 x x x − = − ( ) = + − 2 9 3 3 2 log log .log 2 1 1 x x x ( ) ( ) 2 4 11 .2 8 3 0 log 2 x x x x x + − − − ≥ −       −+−>−+− xxxxx 2 1 log)2(22)144(log 2 1 2 2 2 2 2 2 4.2 2 4 0 x x x x x+ − − − + = ( ) 2 4 2 log 8 log log 2 0 x x x + ≥ 4 2 1162 1 > − −+ − x x x ( ) 2 1 2 2 2 1 3 2 2 3 2 2 x x x x x x − − − − + + > + + ( ) ( ) 1 2 1 2 2 2 5 11 2 24 1 9 2 x x x x x x x + − −   + + − < − − −     D – 2010: 3 3 2 2 2 2 4 4 4 2 4 2 x x x x x x + + + + + − + = + 3 2 3 4 2 1 2 1 .2 2 .2 2 x x x x x x − + − + + − + = + ( ) ( ) 2 2 4 1 1 log 3 4 log 2 x x x < − + − 2 3 2 2 3 3 3 3 2 log 8 log 2 log 3 log 4 x x x x x x x − + − ≥ − + ( ) ( ) 2 2 7 7 2 log log 3 2log 3 log 2 x x x x x x     + + = + +     ( ) 2 2 2 2 3 2 log 3 2 5 log 2 x x x x x x− + ≤ − + − ( ) ( ) ( ) 2 2 2 3 3 3 2log 4 3 log 2 log 2 4 x x x − + + − − = 1 2 3 1 3 2 (9 2.3 3)log ( 1) log 27 .9 9 3 x x x x x + − − − + = − ( ) ( ) 3 2 2 2 2 3 5 5 log 1 log log log .log 1 log 2 log 2 x x x x x + + − + > ( ) 2 2 2 2 2 2 2 34 log 34 15.2 4 2 1 log 2 x x x x x x + + + + = + + + ( ) ( ) ( ) 2 2 6 2 6 log .log 2 log 2log 2 2 x x x x x x     + + = + +     ( ) ( ) 2 2 16 4 log 2 1 log 4 2 x x x x − + < + . - 2012 ðỗ Ngọc Nam_THPT Trung Giã. Phone: 0949088998. Mail: Moonflower35@gmail.com. 1 BÀI TẬP PHƯƠNG TRÌNH, BẤT PHƯƠNG TRÌNH, HỆ PHƯƠNG TRÌNH MŨ VÀ LOGARIT Bài 1. ðưa về cùng cơ số. ( ) ( ) 2 2 2 5 2 2 5 log 2 11 log 2 12 x x x x + + − − = − − . Đ/s : 2 2 5; 2 5 + − Bài 2. Logarit hóa, mũ hóa. 4 1 3 2 2 1 5 7 x x + +     =         2 5 .3 1 x x = 2 1 1 5. 50 x x x − + = 3 2 2 3 x x = ( ) ( ) 2 3 5 7 log log log log x x ≤ 2 2x 3 x 2 x 3 .4 18 − − = Bài 3. ðặt ẩn phụ − − + − + − + = 2 1 1 1 5.3 7.3 1 6.3 9 16 x x x x 16 64 log 2.log 2 log 2 x