ptbpt 1

<span class='text_page_counter'>(1)</span>HAØM SOÁ MUÕ-HAØM SOÁ LOGARIT. Baøi 1 : So saùnh : a/ a= 32000 vaø b= 23000. e/ a= log 2 √ 5. 2 3. b/ a= ( √ 3− 1 ) vaø b= ( √ 3− 1 ) π 0 .75 π 0 .5 ∧ b= c/ a= 3 3. (). d/ a=. −. vaøb= log 2 2,5 ø f/ a= log 13 150 vaø b= log 17 290. 4 5. (). 1 10. 5. g/. 5. 3. Bài 2 : Rút gọn biểu thức : 1, A = (a-4 – b-4) : ( a-2 – b-2). 2, B =. 5, E =. 4. 11. √. x √ x √ x √ x : x 16 ab− 1 ¿2 ¿ −2 −1 3 a . b ¿ . a−1 b a−2 b ¿ 7, G = a −1 . b2 ¿4 . ¿ −2 ab ¿ ¿ 1− log 3a b 9, K = a (0 < a,b  1) (log a b+ log b a+1)log a b Bài 3 : Tính giá trị các biểu thức sau :. (x. 1 4. 1 4. 8. )( x. 1 2. 1 2. 6, F =. 1 6. 1 6. 2 3. 1 2. 2 3. 1 2. 2 4 8, H = log a b + log a b. 3, C =. 4, D =. 4. 5, E = log 3 36 . log √ 6 3 7, G = log 3 2. log 4 3 . log 5 4 . log 6 5 . log 7 6. log 8 7 9, I =. log √ 2 3 . log 1 5. log 25 2. 11, M = 49 13, P =. 1 3. √√√√. 434 5 5 5 5 4 4 6, F = log 3 6 . log 8 9 log 6 2 1 3 . log 25 √ 2 8, H = log 2 5. √. 12, N = 5log 3+log 6. 3. 1. 5. 9. 1 6. 3. 6. ( √3 9 ) 2 log 3 3. 1 6. 4 3. 10, K = 36log 5 +10lg 2+1 −3 log 36. 3 log7 √ 5+ log49 3. 15,T = 81log 5+ 27log 36 +3 4 log. 2 3. (0 < a 1). 2. 0 . 25 ¿0 −3 −2 −¿ 1, A = 103 :10 −1 −3 4 2 . 2 +5 5 ¿. 7. 1 4. 1 3. 1 3. 1 −3 ¿ 27 ¿ 1 −2 ¿ 2 2, B= 0 .7 ¿0 ¿ 5−3 . 252+ ¿ 3−3 ¿3 ¿ 2: 4− 2+ ¿ ¿. √ 5 √5 √ 5 √5 √ 5. 1 4. −y + y )( x + y ) . 4, D= ( a − b )( a +a b +b ) ( a +b )( a −b )( a − a b +b ) 1 3. 3, C = ( √ x − √ x +1)( x + √ x +1)( x − √ x+ 1) 4. 5. 3 4 h/ a=log 1 3 √ 3 ∧b=log 1 √ 32. vaø b=2. √ 9+5. a=3log 4 ∧b=4 log 3. 9. 4. 14, S = 4 2 log 4 16, V = log 2 (5 ) log 3 5. 6. 12. log2 3 +3 log8 5 3. 9.

<span class='text_page_counter'>(2)</span> log 3 135 log 3 5 log 2 2006 2 − 18, Y= √ log 0 .5 4 + log 15 3 log 405 3 log 8 2006 Baøi 4 : Tính : 1, a= log 3 2 .Tính : log 2 3 ; log 3 12 ; log 12 16 ; log 36 √ 4 theo a 2, c = log 5 3 . Tính : log 25 15 theo c 3, a = log 20 3 , b = log 20 5 , c = log 20 7 . Tính log 20 44100 theo a,b,c 6 4, a= log x 27 ,Tính log √ 3 √ x theo a 5, a = lg 5 , b = lg 3 , Tính log 30 5 theo a,b 17, X=. Bài 5 : Chứng minh : log a N ¿3 ¿ 1, log a ¿ ¿ log a c =1+ log a b ( 0 < a,b,c 1 ) 3, log ab c log a x ¿ 2 1 ( 0 < a1, x > 0 ) 5, log a x . log a x= ¿ 2. 10. lg( lg N ) =1 2, 1+ lg(lg N ) 4, log a b . log b c log c a=1 ( 0 < a,b,c 1 ) 6, a log c =c log a ( 0 <b 1 ; a,c > 0 ) b. b. 2. 7, log a d . log b d+ log b d . log c d +log c d . log a d =. log a d . log b d . log c d log abc d. ( 0 <a,b,c 1 ;d > 0 ). logb (logb a ). 8, a log a ( 0 < a,b  1) =log b a 9, log 18 6+log 2 6=2 log 18 6 . log 2 6 10, (log a b+ log b a+2)(log a b − log ab b)log b a −1=log a b log a b+log a c 11, log ac ( bc)= 1+ log a c b. 12,. √ log2 a+ √ log 2 b ≤2. √. log 2. ( a+b2 ). Với a ≥ 1, b ≥ 1. 3 x+ y 1 = (lg x + lg y ) 4 2 a+ b 1 = (log M a+ log M b) 14, Cho a,b > 0 : a2 + b2 = 7ab . CMR log M 3 2 2 2 15, Cho x,y > 0 : x +4y = 4xy . CMR 2 log 2 (x+ 2 y )=3+ log 2 x +log 2 y a+2 b 1 = (lg a+lg b+ lg3) 16, Cho a,b > 0 : a2 + 4b2 = 23ab . CMR lg 3 2 1 17, Cho x,y > 0 : x2 +4y2 = 12xy . CMR log a ( x +2 y )−2 log a 2= (log a x +log b y ) 2 1 1 18 , Cho 2 < 10 , CMR : log π + log π >2 2 5 13, Cho x,y > 0 : 9x2 + y2 = 10xy . CMR. lg. PHÖÔNG TRÌNH – BAÁT PHÖÔNG TRÌNH MUÕ VAØ LOGARIT.

<span class='text_page_counter'>(3)</span> Baøi 1 : Giaûi caùc phöông trình sau : 1/ 3 x +6 x+ 8=1 2. 2. 3/ 2x. −3 x+2. 5/ 2. 2 x −3. 7/ 27. =. 4 x− 12 1 = 6/ ( √ 5 ). ( 25 ). 1− x 2−x. 1 3. (). 2. 2. x +3 x+5. 9/ 5 √ 8 x− 1=500 x +1 2 11/ ( x − 2 ) = ( x −2 ) 13/ 2. 9 x − 3x =3 15/ 9 x −2 . 3x +1+ 9=0. 2. 17/ 32 x +5=3 x+2 +2 19/ 3 x − 4 . 3− x +3=0 21/ 4 . 22 x −6 x =18 .. 32 x 23/ 64 . 9 x −84 .12 x +27 . 16 x =0. 1. 25/ 3 . 4 x+1 − 5 .6 x+1 +2 . 9x +1=0. x. ( √3 3 − √ 8 ) + ( √3 3+ √ 8 ) =6 x. x. 31/ ( 4 + √ 15 ) + ( 4 − √ 15 ) =8 5+2 √ 6 ¿ x ¿ 5 −2 √ 6 ¿ x 33/ ¿ ¿ ¿ √¿ 35/ 7 .3 x+1 −5 x+2=3 x+ 4 − 5x +3 2x 2x x x 37/ 5 =3 + 2(5 +3 ). 41/ x –(3-2 )x + 2(1-2 ) = 0 43/25x –2(3-x)5x + 2x-7 = 0 Baøi 2 : Giaûi caùc baát phöông trình sau : 1/ 22x -3.2x+2 + 32 < 0 3/ 25x < 6. 5x – 5 5/ 5 – 5 7/ 2. 2 x+1. x+1. x. 2/8x  4 ( 4 – 2x) 4/ 4x + 2x+1 – 80 > 0 1 4 x − 15 x+13 3 x − 4 <2 6/ 2 2. (). >4 2 x+3. −21 .. 36/ 73 x +9 . 52 x =25x +9 . 73 x 38/ 22 x −1 +32 x +52 x+1=2 x +3 x+1 +5 x+2 1 x =x+ 4 40/ 3 42/ 9-x –(x+2)3-x - 2(x+4) = 0 44/ 4x +9x + 16x = 81x. (). x. ( 12 ). +2> 0. 1. 34/ 5 x− 1=10 x .2− x .5 x+1. 39/ 3x + x -4 = 0. 2x. 1. 26/ 6 . 9 x −13 .6 x +6 . 4 x =0 x x 28/ ( 2+ √ 3 ) + ( 2 − √3 ) =4 x 7+ √ 48 ¿ ¿ 7 − √ 48 ¿ x 30/ ¿ ¿ ¿ √¿ x x 32/ ( 7+4 √ 3 ) −3 ( 2 − √ 3 ) +2=0. 27/ 5 . 4 x −7 . 10 x +2 . 25x =0. x. x+3. 10/ ( x 2+ 2 ) =( x2 +2 ) 12/ 4 2 x − 5 . 4 x + 4=0 14/ 9 x − 4 x+1 − 3x +2=0 16/ 3 .52 x− 1 − 2. 5 x− 1=0,2 25 x 18/ 5 −24= x 5 x 20/ 9 −2 . 4 x =6 x x 22/ 9 + 6x =22 x+1 24/ 3 .16 x +2. 81 x =5 .36 x. 2. 2. 3− x. 8/ 93 x =3 x +5. xx. 29/. (). 2. =3 x −1. =4. x+2. 2/ 23 x −2=5 1 x− 1 x + 3 x+5 = 4/ 4 2. 8/ 3 .7 2 x − 37. 140 x ≤ 26 .20 x.

<span class='text_page_counter'>(4)</span> 2 (x− 2). 9/ 4 x −22 (x− 1) +8 3 >52 11/ 4x – 2.25x < 10x Baøi 3 : Giaûi caùc phöông trình sau :. 1. 2. 2 2/ log 1 (3 x −5 x )+ 3=0. 1/ log3(2x+5) – 2 = 0. 2. 3/ log 5 (2 x+ 1)+ log 5 (2− x)=0 log 2 (x −5)+ log 1 (2 x+1)=log 2 6 2. 7/ log8x + log64x =. 1. 10/ 25 x+ 2 + 4 x+ 2 7 .10 x 2 x −7 x >1 12/ ( x − 3 ). 4/ log 2 (x +5)− log 2 ( x +2)=1 6/ lg5+lg(x+10)-1= lg(21x-20)-lg(2x-1). 1 2. 8/ log 5 x=log 5 (x +6)−log 5 (x +2). log 5 x+ log 25 x=log 0,2 √ 3 11/ log 2 (x +3)=1+ log2 ( x −1) log x− 1 9 log 2 ¿=0 13/ log 1 ¿. 19/ log 4 ( x+ 3) − log 2 (x −1)=2 − log 4 8 2 2 21/ lg x −3 lg x=lg( x ) −4 log 3 x ¿2 −5 log3 9 x +3=0 23/ 2¿ log ( x −5)+ log 1 (2 x+1)=log 2 6 2 25/ 2. 7 27/ log x 2 − log 4 x + =0 6 1 2 + =1 29/ 4 − lg x 2+ lg x. 2. x 14/ log 2 (9 − 2 )=3 − x. 15/. 16/ log 5 ( x +20). log x √5=1 18/ log 4 (log 2 x)+log 2 (log 4 x)=2 log 3 x+ log √ 3 x +log 1 x=6 20/ 3 22/ log 2 x=log 4 3 x +2 24/ log 1 x −3 log 1 x+ 2=0 3. √. 3. 26/ log 2 x − log x 8=− 2 28/2x – lg(52x +x -2) = lg 4x x 30/ log 3 [ 1+log 3 (2 − 7) ]=1. 18 −2 x =−1 31/ ( x+ 2) log (x +1)+ 4 (x+1)log 3 ( x +1)−16=0 32/ log 4 (18 −2 ). log 2 8 33/ x lg 4 +4 lg x =32 34/ x lg 9 − 4 . 3lg x +3=0 log x 3 x ¿ =27 35/ 36/ 2log x . 5log x =400 x log 3 x +2¿ 37/ 4 lg 10 x − 6lg x =2. 3lg (100 x ) Baøi 4: Giaûi caùc baát phöông trình sau: 2 1/ log 1 (x − 4 x +6)<−2 2/ log 1 (x +1)≤ log 2 (2 − x) 2 3. x. 3. 2. 3. 3. 3. 2. 2. 2. 4 x+ 6 3/ log 1 x ≥ 0 5. 4/ log 12 (2 x+1)>−1. 2 5/ log 8 (x −4 x+3) ≤ 0. 6/ log 3 (log 12 x) ≥ 0. 2 7/ 2 log 8 (x − 2)+ log 1 ( x − 3)> 3. 2 8/ log 1 (x − 6 x+ 8)+2 log 5 (x − 4)<0. 8. 9/. 2. lg x −3 lg x +3 <1 lg x −1. 9/. 2 10/ log x (2 x − 5 x+ 4)=2 12/ log 3 ( log 1 x)=0. 2. 1 log 3 (x −5)− log 3 2− log 3 (3 x − 20) 2 3 2 17/ log x+1 (2 x +2 x −3 x +1)=3. 5/. 5. 10/ lg 2 x> lg x +2.

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