Bài tập Bất phương trình và Logagic

Chuyên đề phơng trình Bất ph ơng trình và Hệ phơng trình mũ Loga rit ph ơng trình và bất ph ơng trình mũ i) ph ơng pháp logarit hoá và đ a về cùng cơ số 1) 5008.5 1 = x x x 2) ( ) ( ) 244242 22 1 +=+ xxxx x 3) 1 3 2.3 + xx xx 2 2 2 4) ( ) ( ) 55 1x 1-x 1-x + + 22 5) 11-x 2 x = + 34x 6) ( ) ( ) 3 1 1 3 310310 + + <+ x x x x 7) 24 52 2 = xx 8) 1 2 2 2 1 2 x xx 9) 2121 444999 ++++ ++<++ xxxxxx 10) 13 12 2 1 2 1 + + x x 11) ( ) 112 1 1 2 + + x x xx 12) ( ) 3 2 2 2 11 2 > + xx xx 13) 2431 5353.7 ++++ ++ xxxx Ii) Đặt ẩn phụ: 1) 1444 7325623 222 +=+ +++++ xxxxxx 2) ( ) ( ) 4347347 sinsin =++ xx 3) ( ) 1 2 12 2 1 2.62 13 3 =+ xx xx 4) ( ) 05232.29 =++ xx xx 5) ( ) 77,0.6 100 7 2 += x x x 6) 1 12 3 1 3 3 1 + + xx = 12 7) 12 3 1 3 3 1 x 2 x 2 > + + 1 8) 1099 22 cossin =+ xx 9) 1 1 2 4 2 2 12 x x x+ + + + = + 10) 2 2 2 1 2 2 2 9.2 2 0 x x x x+ + + + = 11) ( ) ( )( ) ( ) 3243234732 +=+++ xx 12) 06.3-1-7.35.3 1xx1-x1-2x =++ + 9 13) 06.913.6-6.4 xxx =+ 14) 32.3-9 xx < 15) 0326.2-4 1xx =+ + 16) ( ) ( ) 02-5353 2 22 x-2x1 x-2xx-2x ++ + 17) 205-3.1512.3 1xxx =+ + 18) 323 1-x1-2x += 19) ( ) ( ) 1235635-6 xx =++ 20) 0173. 3 26 9 =+ xx 21) 2 4 4 3 8.3 9.9 0 x x x x + + + = 22) 022 64312 = ++ xx 23) ( ) ( ) 43232 =++ xx 24) ( ) ( ) 02323347 =++ xx 25) 111 222 964.2 +++ =+ xxx 26) 12.222 56165 22 +=+ + xxxx 27) 101616 22 cossin =+ xx 28) 0 12 122 1 + x xx 29) xxxx 22.152 53632 <+ ++ 30) 222 22121 5.34925 xxxxxx ++ + 31) 03.183 1 log log 3 2 3 >+ x x x 32) 09.93.83 442 > +++ xxxx 33) 3log 2 1 1 2 4 9 1 3 1 > xx 34) 9339 2 > + xxx 35) xxxx 993.8 44 1 >+ ++ 36) 1313 22 3.2839 + <+ xx 37) 013.43.4 21 2 + + xxx 38) 2 5 2 2 1 2 2 1 log log >+ x x x 39) 0124 21 2 + +++ xxx I II) ph ơng pháp hàm số: 1) 12 21025 + =+ xxx 2) xxx 9.36.24 = 10) ( ) 0331033 232 =++ xx xx 1 Chuyªn ®Ò ph¬ng tr×nh BÊt ph– ¬ng tr×nh vµ HÖ ph¬ng tr×nh mò Loga rit – 3) 2 6.52.93.4 x xx =− 4) 13 250125 + =+ xxx 5) ( ) 2 2 1 2 -2 1 x x x x − − = − 6) 163.32.2 −>+ xxx 7) ( ) x 2 22 32x3x-.2x32x3x- ++−>++− 2525 xx x 8) x x 381 2 =+ ) 5loglog2 22 3 xx x =+ 11) ( ) 2 1 122 2 −=+− −− x xxx 12) 1323 424 >+ ++ xx 13) 0 24 233 2 ≥ − −+ − x x x 14) 3 x + 5 x = 6x + 2 Mét sè bµi to¸n tù luyÖn: 1) 7. 3 x+1 - 5 x+2 = 3 x+4 - 5 x+3 2) 6. 4 x - 13.6 x + 6.9 x = 0 3) 7 6-x = x + 2 4) ( ) ( ) 43232 =++− xx 5) 2 3 1 x x = + 6) 3 x+1 + 3 x-2 - 3 x-3 + 3 x-4 = 750 7) 3 25 x-2 + (3x - 10)5 x-2 + 3 - x = 0 8) ( ) ( ) x xx 23232 =−++ 9)5 x + 5 x +1 + 5 x + 2 = 3 x + 3 x + 3 - 3 x +1 1 ( ) 2 3 3 4 1 2 2 10) 1 1 11)2 4 12)8 36.3 x x x x x x x x − + − − − + + = = = ( ) ( ) 1 14)5 5 4 0 15)6.9 13.6 6.4 0 16) 5 24 5 24 10 x x x x x x x − − + = − + = + + − = ( ) 2 8 1 3 17) 15 1 4 18)2 4 x x x x x− + − + = = 2 5 6 2 1 2 1 2 19)2 16 2 20)2 2 2 3 3 3 x x x x x x x x − + − − − − = + + = − + ( ) ( ) ( ) 2 2 1 1 2 2 2 4 2 2 4 8 2 5 2 6 7 21)2 .3 .5 12 22) 1 1 23) 1 24) 2 2 1 25)3 4.3 27 0 26)2 2 17 0 x x x x x x x x x x x x x x x x − − − − − + + + + = − + = − = − + = − + = + − = ( ) ( ) + + − − = − − = 27) 2 3 2 3 4 0 28)2.16 15.4 8 0 x x x x ( ) 2 2 3 x 3 x 3 x-1 42) 2 .5 0,01. 10 − − = ( ) ( ) + − − + =29) 7 4 3 3 2 3 2 0 x x ( ) ( ) + + + − = 3 30) 3 5 16 3 5 2 x x x 1 1 1 2 3 3 31)3.16 2.81 5.36 32)2.4 6 9 33)8 2 12 0 x x x x x x x x x + + = + = − + = ( ) ( ) 2 1 2 2 1 1 2 2 34)3 4 5 35)3 4 0 36)2 3 5 2 3 5 37) 3 2 2 1 2 0 x x x x x x x x x x x x x x x − + + + + = + − = + + = + + − − + − = ( ) ( ) 2 x x 2 1 1 x 1 3 x 3 1 5 2 x 1 4 x 10 3 1 x-3 3 1 3x-7 1 38) 3.3 . 81 3 39) 2 4 .0,125 4 2 40) 2.0,5 -16 0 41) 8 0,25 1 x x x x x x + + + + + + − −   =  ÷   = = = 2 2 2 2 2 x 12 3 x x 1 x x 1 x 2 2x-1 x-1 1 1 1 x 25 27 43) 0,6 9 125 44) 2 -3 3 -2 45) 3.5 -2.5 0,2 46) 10 25 4,25.50 x x − − − +     =  ÷  ÷     = = + = 2 2 x 1 x 3 x x-1 47) 9 -36.3 3 0 48) 4 -10.2 -24 0 − − + = = hÖ ph ¬ng tr×nh mò vµ hÖ ph ¬ng tr×nh logarit 1) ( ) ( ) 2 2 log 5 log l g l g4 1 l g l g3 x y x y o x o o y o − = − +   −  = −  −  20) ( ) ( ) 1 l g 3 l g 5 0 4 4 8 8 0 y x y x o x o y − − − − =    − =   2 Chuyªn ®Ò ph¬ng tr×nh BÊt ph– ¬ng tr×nh vµ HÖ ph¬ng tr×nh mò Loga rit – 2) ( ) ( ) 3 3 4 32 log 1 log +   =   − = − +  x y y x x y x y 3)      = = +− 5 1 10515 2 xy y xx 4) ( )    =+ = + 323log 2log 1 y y x x 5) ( ) ( )      =+ =+ − − yx xy yx yx 2 2 69 12 2 2 6)    = =− 12 3 3 1log y x xy 7) ( ) 2 4 4 9 27.3 0 1 1 l g l g lg 4 4 2 xy y o x o y x  − =   + = −   8) ( )      =+ = − 2log 11522.3 5 yx yx 10) ( )      =− = 2log 9722.3 3 yx yx 9) ( ) ( ) ( ) 2 2 l g 1 l g8 l g l g l g3 o x y o o x y o x y o  + = +   + − − =   11) ( ) ( ) ( ) ( )    +=−−−− = −+ xyxyxy xy 555 log21 loglog122log2 483 3 12) ( ) ( ) ( ) yxyxyx +=−=+ 3 22 3 33 9 logloglog 13) ( )    =−+ =−+ 0202 1log2loglog 18 ayx ayx aa 14) ( ) ( )      −=+ =+ − yxyx yx xy 5 log3 27 5 3 21) ( ) ( )    =+ =+ 232log 223log yx yx y x 22) ( )      >= += + − 0y 64 5,1 5,2 x xx y yy 23) ( ) ( ) ( ) l g l g5 l g l g l g6 l g 1 l g 6 l g l g6 o x y o o x o y o o x o y o y o + − = + −    = −  + − +  24) ( )      =− =− 1log 1loglog 2 2 xy x x y yxy 25) ( ) ( )    =− −=+ 1loglog 22 yx yxyx yx 26) ( )    =+− = − 9log24 36 6 2 xyx x yx 27) ( ) ( )    =− =−−+ 2 1loglog 22 22 vu vuvu 28) ( )      ≠≠= = 0pq vµ qp y x y x yx a a a qp log log log 29)      =         − =+ 5loglog22 12 1 2 yx yx x y 3 Chuyªn ®Ò ph¬ng tr×nh BÊt ph– ¬ng tr×nh vµ HÖ ph¬ng tr×nh mò Loga rit – 15) ( ) ( )      = + − + − + =+ −− 8 53 542 12 yx yx yx yx xyxy 16) ( ) ( )      >= = 0x 642 2 2 y y x x 17)        =+ =+ − 3 1 52 12 1 log log 2 2 5 2 y x x y y x 18) ( )      >=+ = +− 0x 8 1 107 2 yx x yy 19)        = =+           − 32 05log2log2 2 1 2 xy yx x y 30) ( )      >=− = −− 0x 2 1 16 22 yx x yx 35) ( ) ( ) l g l g l g 4 l g3 3 4 4 3 o x o y o o x y =    =   36) ( )      <=+ = 0a 2222 2 lg5,2lglg ayx axy 37)    =− =+ 1loglog 4 44 loglog 88 yx yx xy 38 ) ( ) ( )      = = −−+ − −− + 137,0 12 162 8 2 2 xxyx yx xyx yx 39)    =− =+ 1loglog 272 33 loglog 33 xy yx xy PH¦¥NG TR×NH Vµ BÊT PH¦¥NG TR×NH LOgrIT 1. ( ) ( ) 5 5 5 log x log x 6 log x 2= + − + 2. 5 25 0,2 log x log x log 3+ = 3. ( ) 2 x log 2x 5x 4 2− + = 4. 2 x 3 lg(x 2x 3) lg 0 x 1 + + − + = − 5. 1 .lg(5x 4) lg x 1 2 lg0,18 2 − + + = + 6. 1 2 1 4 lgx 2 lgx + = − + 7. 2 2 log x 10log x 6 0+ + = 8. 0,04 0,2 log x 1 log x 3 1 + + + = 9. x 16 2 3log 16 4log x 2log x− = 10. 2 2x x log 16 log 64 3+ = 11. 3 lg(lgx) lg(lgx 2) 0+ − = 32. 3 1 2 log log x 0   ≥  ÷  ÷   33. 1 3 4x 6 log 0 x + ≥ 34. ( ) ( ) 2 2 log x 3 1 log x 1+ ≥ + − 36. 5 x log 3x 4.log 5 1+ > 37. 2 3 2 x 4x 3 log 0 x x 5 − + ≥ + − 38. 1 3 2 log x log x 1+ > 39. ( ) 2 2x log x 5x 6 1− + < 40. ( ) 2 3x x log 3 x 1 − − > 41. 2 2 3x x 1 5 log x x 1 0 2 +   − + ≥  ÷   42. x 6 2 3 x 1 log log 0 x 2 + −   >  ÷ +   43. 2 2 2 log x log x 0+ ≤ 44. x x 2 16 1 log 2.log 2 log x 6 > − 4 Chuyªn ®Ò ph¬ng tr×nh BÊt ph– ¬ng tr×nh vµ HÖ ph¬ng tr×nh mò Loga rit – 12. x 3 9 1 log log x 9 2x 2   + + =  ÷   13. ( ) ( ) x x 2 2 log 4.3 6 log 9 6 1− − − = 14. ( ) ( ) x 1 x 2 2 1 2 1 log 4 4 .log 4 1 log 8 + + + = 15. ( ) x x lg 6.5 25.20 x lg25+ = + 16. ( ) ( ) ( ) x 1 x 2 lg2 1 lg 5 1 lg 5 5 − − + + = + 17. ( ) x x lg 4 5 x lg2 lg3+ − = + 18. lgx lg5 5 50 x= − 18. 2 2 lg x lgx 3 x 1 x 1 − − = − 19. 2 3 3 log x log x 3 x 162+ = 20. ( ) ( ) 2 x lg x x 6 4 lg x 2+ − − = + + 21. ( ) ( ) 3 5 log x 1 log 2x 1 2+ + + = 22. ( ) ( ) ( ) ( ) 2 3 3 x 2 log x 1 4 x 1 log x 1 16 0 + + + + + − = 23. ( ) 5 log x 3 2 x + = 24. ( ) 2 8 log x 4x 3 1− + ≤ 25. 3 3 log x log x 3 0− − < 26. ( ) 2 1 4 3 log log x 5 0   − >   27. ( ) ( ) 2 1 5 5 log x 6x 8 2 log x 4 0 − + + − < 28. 1 x 3 5 log x log 3 2 + ≥ 29. ( ) x x 9 log log 3 9 1   − <   30. x 2x 2 log 2.log 2.log 4x 1> 31. 8 1 8 2 2log (x 2) log (x 3) 3 − + − > 45. 2 3 3 3 log x 4log x 9 2log x 3− + ≥ − 46. ( ) 2 4 1 2 16 2 log x 4log x 2 4 log x+ < − 47. 2 6 6 log x log x 6 x 12+ ≤ 48. 3 2 2 2 log 2x log x 1 x x − − > 49. ( ) ( ) x x 1 2 1 2 log 2 1 .log 2 2 2 + − − > − 50. ( ) ( ) 2 3 2 2 5 11 2 log x 4x 11 log x 4x 11 0 2 5x 3x − − − − − ≥ − − 51. + > + 2 3 3 1 log x 1 1 log x 52. + < − + 5 5 1 2 1 5 log x 1 log x 53. − > x 100 1 log 100 log x 0 2 54. 11252 5 <− x logxlog 55. ( ) ( ) ( ) 04221 3 3 1 3 1 <−+++− xlogxlogxlog 56. ( ) xlogxlog x 2 2 2 2 + ≤ 4 57. ( ) ( ) 2 2 5 5 log 4 12 log 1 1x x x+ − − + < 58. ( ) ( ) 12lg 2 1 3lg 22 +−>− xxx 59. ( ) 3 8 2 4 1 −+ xlogxlog ≤ 1 60. ( ) ( ) 2431243 2 3 2 9 ++>+++ xxlogxxlog 61. ( ) ( ) 11 1 1 2 +>+ − − xlogxlog x x 62. ( ) ( ) 2 3 23 33 2 3 43282 xlogxxxlogxlogxlogx +−≥−+− 63. 220001 <+ x log 64. 0 132 5 5 lg < +− − + x x x x 65. 2 1 2 24 2 ≥         − − x x log x MỘT SỐ PHƯƠNG TRÌNH MŨ – LÔGA SIÊU VIỆT 5 Chuyªn ®Ò ph¬ng tr×nh BÊt ph– ¬ng tr×nh vµ HÖ ph¬ng tr×nh mò Loga rit – 3 6 3 2 / 2 2 3 log ( 1) log 2 6 1)2 8 14 2)1 8 3 3)log (1 ) log 4)2 5)log ( 3 ) log − + = − + − + = + = = + = x x x x x x x x x x x x 2 2 2 5 6)log ( 2 3) log ( 2 4)− − = − −x x x x [ ] 2 2 2 log log 5 2 log 2 2 2 2 2 x 2 3 2 7) 3 8) 2.3 =3 9)log ( - 4) log 8(x+2) 10)log 3log (3 1) 1 11)3 4 0 12)3 4 5 13)3 (3 10).3 3 − − + = + + =   − − =   + − = + = + − + − x x x x x x x x x x x x x x x x 2 2 x 2 2 2 x x 6 10 2 0 14)3.4 (3 10).2 3 0 15)log log 1 1 16)4.9 12 3.16 0 17)3 os2x 18)3 6 6 − + = + − + − = + + = + − = = = − + − x x x x x x x x x x c x x 2 1 os2x os lg lg6 19)9 2( 2).3 2 5 0 20)4 - 4 3.2 21)(4 15) (4 - 15) 62 22)4 4 3 23)6 12 24)6 8 10 + + + − + − = = + + = + = + = + = x x x x x x x x c c x x x x x x x x 2 2 25)log 8log 2 3 − = x x 2 2 lg lg5 lg 2 7 3 3 3 1 1 26) lg( 2) 8 2 27) 4 6 9 28)( 1 1 2)log ( ) 0 29)5 50 30) 1000 31)log log ( 2) 32)3log (1 = − + + = − + + − − = = − = = + + + x x x x x x x x x x x x x x x x x x 5 2 log ( 3) 3 2 7 4 12 9 2 ) 2log 33)2 34) log (1 ) log 1 35)log ( ) log 2 36)lg( 6) lg( 2) 4 + = = + = − = − − + = + + x x x x x x x x x x x x BÀI TẬP VỀ PHƯƠNG TRÌNH − BẤT PHƯƠNG TRÌNH − HỆ PHƯƠNG TRÌNH 6 Chuyªn ®Ò ph¬ng tr×nh BÊt ph– ¬ng tr×nh vµ HÖ ph¬ng tr×nh mò Loga rit – MŨ VÀ LOGARIT A. PHƯƠNG TRÌNH MŨ: Bài 1: Giải các phương trình: 1/. 3 x + 5 x = 6x + 2 2/. 12.9 x - 35.6 x + 18.4 x = 0 3/. 4 x = 3x + 1 4/. ( ) ( ) 3 2 2 3 2 2 6 x x x + + − = 5/. ( ) ( ) 2 3 2 3 4 x x + + − = 6/. 2 2 18 2 6 x x + + − = 7/. 12.9 x - 35.6 x + 18.4 x = 0 8/. 3 x + 3 3 - x = 12. 9/. 3 6 3 x x + = 10/. 2008 x + 2006 x = 2.2007 x 11/. 125 x + 50 x = 2 3x + 1 12/. 2 1 1 2 5 x x− + = 13/. 2 2 8 2 2 8 2 x x x x x − + − = + − 14/. 2 2 2 2 2 5 x x x x+ − − + = 15/. 15. x 2 .2 x + 4x + 8 = 4.x 2 + x.2 x + 2 x + 1 16. 6 x + 8 = 2 x + 1 + 4.3 x 17. 2 2 2 ( 1) 1 4 2 2 1 x x x x + + − + = + 18/ 3 x + 1 = 10 − x. 19/. 2. 3 3 1 4 2 5.2 2 0 x x x x+ − + + + − + = 20/. (x + 4).9 x − (x + 5).3 x + 1 = 0 21/. 4 x + (x – 8)2 x + 12 – 2x = 0 22/. 4 3 3 4 x x = 23/. 2 2 2 2 4 ( 7).2 12 4 0 x x x x+ − + − = 24/. 8 x − 7.4 x + 7.2 x + 1 − 8 = 0 B. BẤT PHƯƠNG TRÌNH − HỆ PT MŨ: Bài 1: Giải các phương trình: 1/. 3 2 2 3 x x > 2/. ( ) ( ) 3 2 3 2 2 x x + + − ≤ 3/. 2 x + 2 + 5 x + 1 < 2 x + 5 x + 2 4/. 3.4 x + 1 − 35.6 x + 2.9 x + 1  0 5/. ( ) ( ) ( ) 2 2 1 2 1 2 2 1 . 2 5 x x x + + > + − + 6/. 1 1 4 3.2 8 0 2 1 x x x + + − + ≥ − 7/. 2 2 4 x x− ≤ 8/. 3 1 3 2 3 x x + + − ≥ 9/. 2 x − 1 .3 x + 2 > 36 10/. 2 2 11 2 5 x x + + − ≥ 11/. 1 9 4.3 27 0 x x+ − + ≤ 12/. 2 2 2 3 2 3 2 3 x x x x− − − − ≤ 13/. 1 1 1 4 5.2 16 0 x x x x+ − + − + − + ≥ 14/. 2 3 4 0 6 x x x x + − > − − 15/. 1 6 4 2 2.3 x x x+ + < + 16/. 1 1 1 2 2 2 9 x x + − + < 17/. ( ) 22 1 2 9.2 4 . 2 3 0 x x x x + − + + − ≥ 18/. Bài 9: Giải các hệ phương trình 1/. 2 5 2 1 y y x x  + =   − =   2/. 2 2 3 3 ( )( 8) 8 y x y x xy x y  − = − +   + =   3/. 1 2 6 8 4 y y x x − −  =   =   4/. 3 2 11 3 2 11 x y x y y x  + = +   + = +   5/. 2 .9 36 3 .4 36 y x y x  =   =   6/. 2 2 2 2 3 y x y x x xy y  − = −   + + =   7 Chuyªn ®Ò ph¬ng tr×nh BÊt ph– ¬ng tr×nh vµ HÖ ph¬ng tr×nh mò Loga rit – 7/. 2 4 4 32 x x y y  =   =   8/. 4 3 7 4 .3 144 y x y x  − =   =   9/. . 2 5 20 5 .2 50 y x y x  =   =   10/. 2 3 17 3.2 2.3 6 y x y x  + =   − =   11/. 3 2 1 3 2 1 x y y x  = +   = +   12/. 2 3 1 3 19 y y x x  − =   + =   C. PHƯƠNG TRÌNH LOGARIT. Bài 1: Giải các phương trình: 1/. 3 log log 9 3 x x + = 2/. ( ) ( ) 2 4 1 log 2 1 .log 2 2 1 x x+ − − = 3/. 2 2 2 log 3.log 2 0x x− + = 4/. ( ) ( ) 3 3 log 9 log 3 1 x x x x+ = 5/. ( ) ( ) 5 5 5 1 .log 3 log 3 2 log 3 4 x x x + + − = − 6/. 3 3 log log 2 4 6 x x+ = 7/. ( ) ( ) 2 3 3 log 5 log 2 5x x x− − = + 8/. 2 3 3 log ( 12)log 11 0x x x x+ − + − = 9/. 2 3 3 log log 3 6 x x x+ = 10/. ( ) 2 2 log 4 log 2 4x x+ = + − 11/. 2 2 2 2 2 log 3.log 2 log 2x x x− + = − 12/. 2 3 3 2 3 log .log .log 3 log 3logx x x x x x x+ + = + + 13/. ( ) ( ) 3 2 3.log 2 2.log 1x x+ = + 14/. 3 3 3 log 4 log log 2 2 .2 7. x x x x= − 15/. ( ) ( ) 2 2 2 log 4 log 2 5x x− = 16/. ( ) ( ) 3 27 27 3 1 3 log log log logx x+ = 17/. 3 3 log 2 4 logx x+ = − 18/. 2 3 3 2 log .log 3 3.log logx x x x+ = + 19/. ( ) 2 2 2 4 2.log log .log 7 1x x x= − + 20/. ( ) ( ) ( ) 3 3 3 2 log 2 2 log 2 1 log 2 6 x x x+ − + + = − 21/. ( ) 2 2 2 2 8 2 log log 8 8 x x+ = 22/. 2 2 2 log log 6 6.9 6. 13. x x x+ = 23/. ( ) ( ) 2 2 2 2 2 2 log log .log 1 2 3.log 2.log 1x x x x x+ − + = + − 24/. 2 2 log log 3 3 18 x x+ = 25/. 2 2 2 .log 2( 1).log 4 0x x x x− + + = Bài 2: Tìm m để phương trình ( ) ( ) 2 2 log 2 logx mx − = có 1 nghiệm duy nhất. Bài 3: Tìm m để phương trình 2 2 2 2 log log 3x x m − + = có nghiệm x∈ [1; 8]. Bài 4: Tìm m để phương trình ( ) 2 log 4 1 x m x − = + có đúng 2 nghiệm phân biệt. Bài 5: Tìm m để phương trình 2 3 3 log ( 2).log 3 1 0x m x m − + + − = có 2 nghiệm x 1 , x 2 sao cho x 1 .x 2 = 27. Bài 6: Cho ph¬ng tr×nh: 0121 2 3 2 3 =−−++ mxlogxlog (2) 1) Gi¶i ph¬ng tr×nh (2) khi m = 2. 2) T×m m ®Ó ph¬ng tr×nh (2) cã Ýt nhÊt 1 nghiÖm thuéc ®o¹n       3 31; 8 Chuyªn ®Ò ph¬ng tr×nh BÊt ph– ¬ng tr×nh vµ HÖ ph¬ng tr×nh mò Loga rit – D. BẤT PHƯƠNG TRÌNH − HỆ PT LOGARIT. Bài 1: Giải các bất phương trình: 1/. ( ) ( ) 2 4 4 2 log log log log 2x x+ ≥ 2/. 2 2 log 3 log 1x x+ ≥ + 3/. ( ) ( ) 2 2 2 log 3 2 log 14x x x− + ≥ + 4/. ( ) 2 2 2 3 log 2 log 1x x− ≤ 5/. ( ) 2 1 log 4 2 x x x + − ≤ 6/. ( ) 2 2 2 2 log 2log 3 5 4 0x x x x+ − − + ≥ 7/. 2 2 log 1 3 logx x− ≤ − 8/. 2 2 log 1 2 log 2 2. 3 x x x+ ≤ 9/. ( ) ( ) 2 2 2 log 6 5 2 log 2 x x x − + ≥ − 10/. 2 2 2 2 log log 2 0 log 2 x x x − − ≥ 11/. 2 1 1 2 2 log log log 3 1x x    ÷ + − ≤  ÷   12/. 2 2 3 3 2 log .log 2 log logx x x x+ ≤ + 13/. 2 2 2 log log 1 8 x x x   + ≥  ÷   14/. 2 3 3 log log 3 6 x x x+ ≤ Bài 2: Giải các hệ phương trình 1/. 2 2 6 log log 3 x y x y + =   + =  2/. ( ) 2 2 2 3 3 log 6 4 log log 1 x y x y  + + =   + =   3/. log log 2 6 yx y x x y + =    + =   4/. 2 2 2 6 log 3 log log 2 x y x y + =    + =   5/. ( ) ( ) 2 2 3 5 3 log log 1 x y x y x y  − =   + − − =   6/. 2 2 log 4 2 log 2 x y x y + =   − =  7/. 2 3 log log 2 3 9 y y x x  + =   =   8/. 2 2 2 2 log log 16 log log 2 y x x y x y   + =  − =   9/. ( ) ( ) log 2 2 2 log 2 2 2 x y x y y x + − =   + − =   10/. 2 2 2 4 2 log log 3. 2. 10 log log 2 y x x y x y  + =   + =   11/. 32 log 4 y xy x =    =   12/. ( ) 2 2 log 4 log 2 xy x y =     =  ÷     9 . Chuyên đề phơng trình Bất ph ơng trình và Hệ phơng trình mũ Loga rit ph ơng trình và bất ph ơng trình mũ i) ph ơng pháp logarit hoá và đ a về cùng cơ. x x x BÀI TẬP VỀ PHƯƠNG TRÌNH − BẤT PHƯƠNG TRÌNH − HỆ PHƯƠNG TRÌNH 6 Chuyªn ®Ò ph¬ng tr×nh BÊt ph– ¬ng tr×nh vµ HÖ ph¬ng tr×nh mò Loga rit – MŨ VÀ LOGARIT