Phương pháp 1 ! ! = 1. " # # $ % #%$ &$ ' x x x+ + + − − = 2. " # # # # &( ) *( ) & " x x x x+ + + + = − 3. & " & ( " # " # " " " " x x x x x x − + − + + − + = + 4. ( ) " " " # # ( " " # x x x x + + − + = + 5. " & & & # ) "% +# & x x x x − + = ÷ 6. 2 x x 8 1 3x 2 4 − + − = 7. 2 5 x 6x 2 2 16 2 − − = 8. x x 1 x 2 x x 1 x 2 2 2 2 3 3 3 − − − − + + = − + 9. x x 1 x 2 2 .3 .5 12 − − = 10. 2 2 x 1 (x x 1) 1 − − + = 11. x x 1 x 2 x x 1 x 2 5 5 5 3 3 3 + + + + + + = + + 12. 13. 14. 15. 16. 17. 18. 19. 20. & + " ( +" & − − = x x 21. "#"# &&&$$$ ++++ ++=++ xxxxxx 22. ( ) & " ) " """" " +−=+− − xxxx x 23. ( ) " , # " , "" xx x x x x +=+ + 24. "&#""( &"&" +−++ = xxxx 25. Phương pháp 2-./0 1234567895:;<9=02>56? 4 =⇒ "4 = " @ &4 = & @A@ 4 # # = ÷ A B392 " C=2C " ='@2 & C=2 " C2 " C & ='B, " & !@D 2 = # " " " # " ( $" * ' x x x x+ − − + − − − = " & ", # , ( %( " ' x x+ + − − = & ( ) ( ) ( ) "* #$ & " % ( & " " & # x x x + + + − − = ( ( ) ( ) " & " & #( x x − + + = $ & # $ & $" &" % ' x x − − − + = * & & # + # " * " # " " x x x x− − − − = ÷ ÷ "% #" "+ x x x + = ) #'& ) ' x x − + = " " ( *" + ' x x − + = " " " #$"$ &(#$ #$) ' x x x − + = " " , ) ) #' x x + = ( ) ( ) " & " & ( x x + + − = ! & $ 5, 5, & " x x + = " +" &5,5, " " $ ' xx x x − + − = # ( ) ( ) " & " & " x x x + + − = $ # " $ $'" "* x x− − + = % "$ #"" *"$'#* ' x x x − − = # & & *( " #" ' x x + − + = 5, 5,$ "$ $ ( x x= + # ( ( &" x x x x+ + − = " " , " $" % x x + = " ," , ( ( & x x + = ! ( ) ( ) ( #$ ( #$ + x x − + + = " 4x 8 2x 5 3 4.3 27 0 + + − + = # 2x 6 x 7 2 2 17 0 + + + − = $ x x (2 3) (2 3) 4 0+ + − − = % x x 2.16 15.4 8 0− − = x x x 3 (3 5) 16(3 5) 2 + + + − = x x (7 4 3) 3(2 3) 2 0+ − − + = x x x 3.16 2.8 5.36+ = 1 1 1 x x x 2.4 6 9+ = 2 3x 3 x x 8 2 12 0 + − + = ! x x 1 x 2 x x 1 x 2 5 5 5 3 3 3 + + + + + + = + + " ( ) ( ) , , $ % ( & % ( & " x x + + − = # ( ) ( ) % & $ % & $ #(" x x x + + − = ) +& % ' x x − + = $ " # # # ( "# #&( " x x− − + = % # # # *) #&* *( ' x x x − + = & & & "$ ) #$ ' x x x − + = 2x 8 x 5 3 4.3 27 0 + + − + = x x x 6.9 13.6 6.4 0− + = x x ( 2 3 ) ( 2 3 ) 4− + + = &"" " " " =− −+− xxxx ! '"%"#+#"(+& =−−+ xxxx " '%%#()"" "" =+− xxx # % & $ % & $ % + " " + − + = ÷ ÷ $ ( ) ( ) " & " & "+ + − = % & & #! # #" " *" # " " − − − + = 0455 1 =+− − xx 16 5 202222 22 =+++ −− xxxx ( ) ( ) 10245245 =−++ xx ( ) ( ) 3 2531653 + =−++ x xx ( ) ( ) 02323347 =+−−+ xx ! ( ) ( ) 14347347 ≥++− xx " ( ) ( ) 43232 =++− xx # ( ) ( ) 10625625 tantan =−++ xx $ xxx /1/1/1 964 =+ % 104.66.139.6 =+− xxx ! " # $ !% ! ! E"@ E$F( ! E# ! E# EG# ! E " 5, & !! E"@ E" !" H74I E# !# JK !$ " " &#* & #'!( & x x x x − − + − + − L/MN,O,O! "% ( ) ( ) '"%$&$& =−++− x xx " xxx "%"#++ =+ " '"'"+ &&" =−+ + x x x " # " #" " # "*" !#& & =+−− − xx xx " *(!$#"$"%$)$ & =+++ −− xxxx " xxx )#&&( #& −=− + "! ')&*#&%&$ ###" =+−+− +−− xxxx "" $55 $'$ x x −= "# "(""& ""#"&"( ++ +−=− xxxx "$ ( ) ( ) ( ) &" ( &"&" #"# " " − =−++ −−− xxx #% Phương pháp3PQRST5O4U=K,D K?=V99M9NMK./0KW=02>XM9S T! # 8.3 x + 3.2 x = 24 + 6 x " '(""(" " "" =+−− −+ xxxxx & "'$#$&&#" # =−+ +xxx ( $ ( ) '")&)"& " =++− xxxx * ( ) ( ) '"#""& " =−+−− xx xx % ( ) '$"&"") =−+−+ xx xx + ( ) '&$#'&"$& "" =−+−+ −− xx xx ) ( ) #""( " "" ## +=+ +−+ xxxx #' xxx *#&" +=+ Phương pháp41NY/M5OPZ95:;<M91N02;0 .[4: 2 ! ! ! 5, = ! !5, = !5, !5, = + + + # ( # & " " # $ % x x+ + = ÷ ÷ " " $ & # x x = & " & + * x x x+ = ( # " # () & " x x− + = $ " " " & #$ x x x− = * " # # $ " $' x x x − + = % & " & " * x x x+ = + & " " & x x = ) #' ## #" #& # $ + #'' x x x+ = #( " " & " * " $ " & & " x x x x x x+ + − + − − = − #$ Phương pháp 5HT/P72ZO4 C !=4 \.474 ' B>4 !]=,D^=⇒ , 5O742;_ C != ! \.474 , B>4 !]=` !^=,D !^=` !]=! ⇒ , 5O742;_ C2!=!@ B>4 !]=,D^=⇒⇔2= C !=' \.4?74 # @ " B>4 !56/aab',Dc'!⇒a !]=,D=!⇒a !='W MNd294U74⇒ !='WMNd2974⇒W74 # @ " e-#f # " " # & x x = + " & " " + #( x x x − = − + − VD2.JK9f " 5, &x x= − " ( ) " " " 5, # 5, * "x x x x+ − = − VD3.JK9f # ( ) "$ " & $ " % ' x x x x− − + − = " & + " " ' x x x x − − + − = VD4.JKf ( ) " & " & & #" % + #) #" x x x x x x x+ − = − + − + 1. ( ) "$ x x x + = 2. ( ) " " &"$ & #' $ & ' x x x x − − + − + − = 3. ( ) ) " " & " $ ' x x x x+ − + − = 4. x x x 3 4 5+ = 5. x 3 x 4 0+ − = 6. 7. x x 4115 =+ 8. 132 2 += x x 9. x xxx 202459 ++= 10. 2112212 532532 +++− ++=++ xxxxxx 11. 9,2 5 2 2 5 /1 = + xx 12. x x x x x x 2 2 22 22 2 211 − =− −− 13. ( ) ( ) 021223 2 =−+−− xx xx 14. 20515.33.12 1 =−+ +xxx 15. 16. 17. E# 18. E# E" 19. 20. ( ) & " & "! $! x x x − + + = eN74 21. # " ( # x x x + − = − 22. " " & # x x = + 23. &'(')*&+'*, %/ 24. ( ) " ## #"( " −=− −− x xx 25. x x x x x # " # "" "" " "## −=− −− 26. x xxxx &,%"" &"" ,(,& =− ++ 27. ( ) ( ) #&(%&" # −=+−+ + x xx 28. ( ) ( ) ( ) xxx $""&$% =+++ 29. ( ) xx xx "#"( " " ++−= 30. x x * "#%) =+ 31. Phương pháp 699 eg=eh B4egiQ@ehjQ;egjQ@ehiQ! h⇔eg=eh=Qk> K;! # #"&""& ##"" +++=++ ++ x xxx xx Hd " #≥ + 2. ( ) x x x + += # ", "" " 3. x x ",& " = 0123 '45&+678&'59:& = 5, = = ⇔ = 'cl# = 5, ! = ! = ⇔ = 'cl#@m !Wn D=7 ! 'e ! ' 5, ! 5, ! ! ! > > = ⇔ = @'cl#! ;6<=>'45&+>'?>+*:*>'45&+678&'@A+)7*6 Phương pháp 1 5, ! 5, != B3f =5, @5, !C5, !=5, ! !! 1. xx 3322 loglogloglog = 2. xx 234432 loglogloglogloglog = 3. xxx 332332 loglogloglogloglog =+ 4. 5. 6. 7. 8. 9. E#* 10. 11. E#@ E*5,! 12. 13. 14. + + = − − x x 1 log (4 4) x log (2 3) 2 1 2 15. !&5,!(5,!#5, " # " " # " " xxx −=++− 16. 17. 18. 19. ( ) (5 " #*5 ( # ""&5 ( x xx −+=− − 20. '"%&5&5 " # #"5" # = +− ++ x x 21. ( ) ( ) *"5,#(5, & "" −+=+ +xx x 22. ( ) ( ) " ( # "%#5, #" #" # xx x x −+ −= − 23. ( ) [ ] { } " # 5,,#5,"5, &"&( =++ x 24. ( ) ##"5,5,5," && " ) −+= xxx 25. ( ) " # "#&5, " & =+−− + xx x 26. ( ) ( ) & + " " ( (5,(5,"#5, xxx ++−=++ 27. ( ) ( ) ( ) ( ) #5,#5,#5,#5, "( " "( " " " " " +−+++=+−+++ xxxxxxxx 28. ( ) ( ) " ) & & " "% &5, " & 5, " # *$5, −+ − =+− x x xx 29. + ( " " # # 5, &! 5, #! 5, ( ! " ( x x x+ + − = 30. & & " & " & # 5, 5, 5, 5, " & x x x x − = + 31. $ # "5, #! 5, 5, " x x− = − 32. " " " 5, &! 5, * #'! # ' f & x x DK x − − − + = > 33. " # 5 #'! 5 " 5( " + + = −x 34. " " & " " # 5, " ! 5, & " " x x x x+ − = − 35. & " 5, #" " " " & " 5, #! 5, x x x x + − = + − 36. " " & & 5, "! 5, ( ( )x x x+ + + + = Hf E"$@ EG") 37. ( 5, "!5, " # x x + = 38. " " " " " 5, & "! 5, % #"! & 5, &x x x x+ + + + + = + 39. (Chưa gii đưc) 40. 41. 42. 43. '!(5,!"5," " && =−+− xx 44. '!5,!"## " " =−−++− xxxx @ 45. 2 3 4 8 2 log (x 1) 2 log 4 x log (4 x)+ + = − + + 46. xxxx "*5,!#5, " " " −=−+ -./04: ( ) xxx ( ( * 5,5," =+ ( ) xx $% 5,"5, =+ ( ) xx &" 5,#5, =+ " " & " 5, " #! 5, " !x x x x+ + = + Phương pháp 2-./0 1234567895N9=02>56? ( ) ( ) #$$5,#$5, # "$$ =−− +xx #! " 5, #* 5, #! x x + = + " " " 5, ( 5, #" x x x = " ( 5, ( 5, $ 'x x− − = # 5, 5, @5, @5, @5, = ⇒ = = = = @eX'c l#@b'! 3 3 2 2 4 log x log x 3 + = '$#5,5, " & " & =−++ xx Phương pháp3PQRST5O4U=K,D K?=V99M9NMK./0KW=02>XM9S T! 2 7 2 7 log x 2.log x 2 log x. log x+ = + Phương pháp 4HT/P72ZO4 C !=4 \.474 ' B>4 !]=,D^=⇒ , 5O742;_ C != ! \.474 , B>4 !]=` !^=,D !^=` !]=! ⇒ , 5O742;_ C2!=!@ B>4 !]=,D^=⇒⇔2= C !=' \.4?74 # @ " B>4 !56/aab',Dc'!⇒a !]=,D=!⇒a !='W MNd294U74⇒ !='WMNd2974⇒W74 # @ " ( ) " " " 5, # 5, * "x x x x+ − = − 2 2 2 log (x x 6) x log (x 2) 4− − + = + + ! " # ( ) ( ) " 5, * ( 5, "x x x x+ − − = + + $ ( ) ( ) ( ) ( ) " & & & 5, " ( " 5, " #*x x x x+ + + + + = % #("#% $(" & 5, " " " & ++= ++ ++ xx xx xx & & & 5, 5, # 'x x− − = " " " 5, #!5, " * 'x x x x+ − + − = [...]...www.VNMATH.com 13 2 x 2 +1 log 2 ( x + 1) = 4 2 x +1 (log 2 x + 1 + 1) 14 Phương pháp 5 Đánh giá Đưa phương trình vế dạng VT =VP Cm VT ≥ M; VP ≤ M (hay VT ≤M; VP ≥M) Phương trình ⇔ VT=VP=M (Đẳng thức xảy ra) . Phương pháp 1 ! ! = 1. ". ) " , # " , "" xx x x x x +=+ + 24. "&#""( &"&" +−++ = xxxx 25. Phương pháp 2-./0 1234567895:;<9=02>56? 4 =⇒ "4 = " @ &4 = & @A@ 4 #. x x −= "# "(""& ""#"&"( ++ +−=− xxxx "$ ( ) ( ) ( ) &" ( &"&" #"# " " − =−++ −−− xxx #% Phương pháp3 PQRST5O4U=K,D K?=V99M9NMK./0KW=02>XM9S T! #