Ko'rsatgichli va logarifim

1. 25log5x − 52log2𝑥 = 24
9. Tengsizlikni yeching:
tenglamaning ildizi a bo’lsa a2-5a+7 ni toping.
(7x+1 − 1)(2x − 4)
>0
x−2
A) 33
B) 32
4𝑥+5
4
2. (√2)
= (√2)
C) 31
D) 30
−2𝑥
3
15
B) −
16
B) (2; +∞)
C) (−1; 2) ∪ (2; +∞)
D) (−∞; −1) ∪ (2; +∞)
2
10. 42𝑙𝑔x + 112𝑙𝑔x = 3
tenglamani yeching.
A) −
A) (−1; +∞)
21
C) −
16
9
16
D) −
17
16
tenglamani yeching.
3. Tengsizlikni yeching:
A) 0,1
B) 10
C) 100
3|𝑥| − 27
≥0
𝑥−3
11. Agar 4x = 125 va 8𝑦 = 5 bo’lsa,
B) [−3; +∞)
A) -6
B) 8
C) 6
12. 𝑙𝑜𝑔32 (27x) = 𝑙𝑜𝑔3 x 6
4. Hisoblang:
tenglamaning ildizini toping.
10 (3log. √34 − 72𝑙𝑜𝑔3438 + 12): 7𝑙𝑜𝑔49196
A) haqiqiy ildizga ega emas
B) 27
A) 25
C) 9
D) 3
B) 20
C) 35
D) 42
3 9
− 𝑙𝑜𝑔3 (𝑙𝑜𝑔2 √ √2) + 1.
B) 12
C) 9
D) 6
6. 733x+1 − 5x+2 = 3x+4 − 5x+3
tenglamaning ildizi quyidagi oraliqlardan qaysi
biriga tegishli?
A) (0; 1]
B) (−2; −1] C) (−1; 0]
D) (0; 2]
7. Agar 𝑓(x) = 𝑙𝑜𝑔2 x 3 + 1 bo’lsa,
B) 2
3
C) √4
x+3
C) (−∞; −1]∪(3;+∞)
D) 7
C) 2
D) 1
𝑙𝑜𝑔4 28  𝑙𝑜𝑔7 28
𝑙𝑜𝑔4 7 + 𝑙𝑜𝑔7 4 + 2
A) 3
B) 0
3x+1 +3x+2 +3x+3
5x+2 +145x
D) 2√2
B) 1,44
C) 9
D) 0,36
16. lg (𝑙𝑜𝑔3 (2 + 𝑙𝑜𝑔3 (x − 2))) = 0
tenglamaning ildizi x0 bo’lsa, 3x0-2 ning
1
16
A) (−∞; −1]
C) 4
14. Hisoblang:
A) 25
8. Tengsizlikni yeching:
4x−3 ≤
B) 6
funksiya berilgan bo’lsa, 9·f(−2) ni hisoblang.
tenglamani yeching.
4
A) 5
15. 𝑓(x) =
1
𝑓(2) + 𝑓 ( ) = 𝑓(x)
x
A) √8
ni
13. Agar 3x + 33−x = 12 tenglamaning
ildizlari x1 va x2 bo’lsa, x1+ x2+ x1 x2 ni
hisblang.
5. Hisoblang:
A) 11
𝑦
D) -8
C) (−∞; 3) ∪ (3; +∞) D) [−3; 3) ∪ (3; +∞)
7
2x−y
toping.
A) [0; 3) ∪ (3; +∞)
1
𝑙𝑜𝑔64 49
D) 0,01
qiymatini toping.
A) 5
B) [1; 3)
D) (3;+∞)
17. 𝑏 =
B) 13
1
10−𝑎
ifodalang.
va 𝑐 =
C) 10
1
10−𝑏
D) 7
bo’lsa a ni c orqali
A) a=c
B) a=lglgc C) a=lgc
D) a=10
26. Tengsizlikni yeching:
18. Hisoblang:
|x − 6| (𝑙𝑜𝑔1 (x − 2) + 1) < 0
3
√(𝑙𝑜𝑔2 3 + 4𝑙𝑜𝑔3 2 − 4)𝑙𝑜𝑔2 3 + 𝑙𝑜𝑔2 12
B) 𝑙𝑜𝑔2 9
A) 4
19. Ushbu 2
√5+x
C) 2
= 42
√x−3
D) 8
tenglamaning
ildizi x0 bo’lsa, x02-2x0 ni hisoblang.
A) 13
B) 11
C) 12
A) (5; 6) ∪ (6; ∞)
B) (2; 5)
C) (5; ∞)
D) (2; 6) ∪ (6; ∞)
27. 2x = 2 − x tenglama nechta haqiqiy ildizga
ega?
D) 10
20. Tengsizlikni yeching:
𝑙𝑜𝑔1 (𝑙𝑜𝑔2 (2 − x)) ≥ 0
A) 1
B) 2
C) yechimga ega emas
D) aniqlab bo’lmaydi
28. Agar 𝑙𝑜𝑔20 250 = 𝑚, bo’lsa 𝑙𝑜𝑔2 5 ni m
2
A) (1;2)
B) [−6;2)∪(2;∞)
orqali ifodalang.
C) [−6;2)
D) [−6;1]
A)
21. 82
=
A) 10
B) 9
8x+5
5
√16x+100
tenglamani yeching.
C) 11
D) 12
2𝑚−1
B)
𝑚−3
1−2𝑚
𝑚−3
tenglamani yeching.
A) (−∞; ) ∪ (28; ∞)
3
A) 3
3
B) 2
4
C) 3
6
3
2
D) 2
1
3
23. Ushbu
x 4 5x + 25 ≥ 25x 4 + 5x
tengsizlikni yeching.
A) (−∞; 1] ∪ [2; ∞)
B) (−∞; 1] ∪ [1; ∞)
C) (−∞; −1] ∪ [1; 2]
D) [−1; 1] ∪ [2; ∞)
24. 𝑦 = 𝑙𝑜𝑔33 x − 12
funksiyaning qiymatlar to’plamini toping.
A) (12; ∞)
B) (−∞; ∞)
C) (0; ∞)
D) (−∞; 12)
25. Tengsizlikni yeching:
392x + 29x − 1 ≤ 0
A) (−∞; −0, 5]
B) (−∞; 2) ∪ [3; +∞)
C) (−∞; ∪ − 2)
D) [0, 5; +∞)
𝑚−2
D)
2𝑚−3
𝑚−2
tengsizlikning barcha haqiqiy yechimlari
to’plamini toping.
1
1−3𝑚
29. 𝑙𝑜𝑔32 (𝑥 − 1) − 2𝑙𝑜𝑔3 (𝑥 − 1) > 3
22. 𝑙𝑜𝑔2 (1643(1−x)+1 ) + 1 = 0
1
C)
3
C) (1; )
4
B) (28; +∞)
3
D) (1; ) ∪ (28; +∞)
4
30. Tengsizlikni yeching:
25𝑙𝑜𝑔5(x−2) + (x − 2)2 > 32
A) (6; ∞)
B) (−∞; −2) ∪ (6; ∞)
C) (2; 6)
D) (2; 6) ∪ (6; ∞)
39. 𝑙𝑜𝑔22 (8x) = 3𝑙𝑜𝑔2 x + 27
32. Hisoblang:
𝑙𝑜𝑔4 28𝑙𝑜𝑔7 28
𝑙𝑜𝑔4 7 + 𝑙𝑜𝑔7 4 + 2
A) 3
34. y=√
B) 0
2
lg(x−2)
C) 2
tenglamaning ildizlari ko’paytmasini toping.
A)
D) 1
−3−1
1
B)2
4
C)4
D)
1
8
40. 𝑦 = 3x−3 + 12
funksiyaning qiymatlar sohasini toping.
funksiya grafigi abssissalar o’qini qaysi
nuqtada kesib o’tadi?
A) (102; 0)
B) kesib o’tmaydi
C) (0; 102)
D) √10 + 2; 0)
A) [13; ∞)
B) (−∞; ∞)
C) (12; ∞)
D) [12; ∞)
41. Agar
𝑓(x + 2) = 𝑙𝑜𝑔3 (x 2 − 6x + 27) + 6
35. Ushbu
bo’lsa, f(2) ning qiymatini toping.
(
x2 −(2x+1)2
2
3 √3 − 1
A) 6 + 𝑙𝑜𝑔3 7
≤1
)
B) 6 + 𝑙𝑜𝑔3 19
C)9
D)8
42. Tengsizlikni yeching:
tengsizlikni yeching.
|2
2
A) [−1; − ]
x+1
3
5
11
− |<
2
2
3
1
B) [−1; − ]
A) (−∞; 8)
3
2
C) (− ; −1] ∪ [− ; )
B) (8; +∞)
1
C) (−∞; )
3
D) (0; 8)
8
1
D) (− ; −1] ∪ [− ; )
43. 𝑦 = 𝑙𝑜𝑔1−2x (2 − √3 − x)
36. 𝑓(x) = 8𝑙𝑜𝑔2x−2
funksiyaning aniqlanish sohasini toping.
funksiyaning qiymatlar sohasini toping.
A) (0; 0,5)
B)(−1; 0,5)
A) (0; +∞)
B) (−2; +∞)
C) (0;0,5) ∪ (0,5;3]
D) (−1; 0) ∪ (0; 0,5)
C) (−∞; +∞)
D) (−2; 0) ∪ (0; +∞)
44.
3
37. x 𝑙𝑜𝑔2x−5 =
1
tenglamani yeching
64
tenglama ildizlarining ko’paytmasini toping.
A) 16
−2x
9−4x−3 = 91,5 (9√3)
B) 64
C)
1
4
D) 32
A) 2
tenglama yechimga ega bo’ladigan p ning
C) -2
D) -3
45. Hisoblang:
𝑙𝑜𝑔3 12 + 𝑙𝑜𝑔4 12 1
+ 𝑙𝑜𝑔2 4
𝑙𝑜𝑔3 12𝑙𝑜𝑔4 12
2
38. Ushbu
3x − p
=0
x−2
B) 3
A) 0
B) 3
C) 1
D) 2
46. Ushbu
√6𝑥 − 𝑥 2 (2𝑥 − 5) > 0
barcha qiymatlarini toping.
A) (−∞; 9) ∪ (9; ∞)
B) (9; ∞)
tengsizlikni nechta butun son qanoatlantiradi?
C) (0; 2) ∪ (2; ∞)
D) (0; 9) ∪ (9; ∞)
A) 3
B) 0
C) 4
D) cheksiz ko’p
𝑙𝑜𝑔3 153 𝑙𝑜𝑔3 459
−
𝑙𝑜𝑔51 3
𝑙𝑜𝑔17 3
47. 𝑦 = √6 − 𝑥 + 𝑙𝑜𝑔4−𝑥 (𝑥 2 − 4)
funksiyaning aniqlanish sohasini toping.
A) 0
A) (2; 3) ∪ (3; 4) ∪ (4; 6)
B) (−∞; −2) ∪ (2; 3) ∪ (3; 4)
qaysi biriga tegishli?
48. Tengsizlikni yeching:
A) (0; 1]
2𝑥+2 − 24
≥1
2𝑥+1 − 8
B) (0; 2)
C) (−∞; 2) ∪ [3; +∞)
D) ( ; +∞)
D) (0; 2]
𝑙𝑔3+𝑙𝑔5
5𝑙𝑔25−𝑙𝑔5
1
A) 5
2
1
4
C) 4
4
1
D)5
2
C) 1
D) 15
31+𝑙𝑜𝑔4 5 4𝑙𝑜𝑔53 5𝑙𝑜𝑔34
3𝑙𝑜𝑔54 4𝑙𝑜𝑔35 5𝑙𝑜𝑔43
tenglama ildizlarining yig’indisini toping.
1
B) 10
56. Hisoblang:
49. 𝑙𝑜𝑔2 (𝑥 − 1) + 𝑙𝑜𝑔𝑥−1 = 1
2
B) (−2; −1] C) (−1; 0]
55. Hisoblang:
A) (2; +∞)
B)4
D) 3
tenglamaning ildizi quyidagi oraliqlardan
D) (−∞; −2) ∪ (2; 4)
1
C) 1
54. 73𝑥+1 − 5𝑥+2 = 3𝑥+4 − 5𝑥+3
C) (2; 4)
A) 6
B) 2
50. Ushbu
A) 3
B) 4
C) 2
D) 1
57. Ushbu
𝑥2
1 𝑥
1 𝑥
( ) − ( ) ≤ 12
4
2
9 3𝑥+5
27 1+ 3
>( )
( )
4
8
tengsizlikning (−4; 4) oralig’idagi butun
yechimlar sonini toping.
tengsizlikni yeching.
A) (−∞; −1)
B) (−1; 7)
C) (7; +∞)
D) (−∞; −1) ∪ (7; +∞)
51. Agar 0 < a < 1 bo’lsa, quyidagilardan
qaysi biri ma’noga ega?
A) 𝑙𝑜𝑔2 𝑙𝑜𝑔𝑎 (𝑎 + 1)
B) 𝑙𝑜𝑔𝑎 𝑙𝑜𝑔𝑎
C) 𝑙𝑜𝑔2 𝑙𝑜𝑔𝑎 𝑙𝑜𝑔2 3
D) 𝑙𝑔𝑙𝑔𝑙𝑔𝑎
𝜋
4
A) 3
A) (3; 4) ∪ (4; 6]
B) (−7; −6] ∪ [6; 7)
C) (3; 7)
D) [6; 7)
59. Ushbu
𝑦 = √22𝑥 − 32𝑥+1 − 16
≥1
tengsizlikni yeching.
funksiyaning aniqlanish sohasini toping.
A) x ≤ 1, x ≥ 4
B) x ≥ 3
D) x ≥ 2
A) (−∞; 8]
B) [8; ∞)
C) x ≤ 2, x ≥ 3
C) (−∞; 2) ∪ (2; 8]
D) (2; 8) ∪ (8; ∞)
60. 𝑙𝑜𝑔2 (𝑥 + 1) + 𝑙𝑜𝑔2 (8 − 𝑥) > 3
53. Hisoblang:
D) 6
tengsizlikni yeching.
𝑥 2 −10𝑥+16
𝑥−2
C) 5
58. (𝑥 − 3)𝑙𝑜𝑔𝑥−3 (49 − 𝑥 2 ) ≤ 13
52. Ushbu
(√5 − 2)
B) 2
tengsizlikni yeching.
A) (0; 7)
B) (7; 8)
C) (−1; 0) ∪ (7; 8)
D) (−1; 8)
A) 16
B) 4
C) 10
61. 𝑓(𝑥) = 3|𝑥| − 2 funksiyaning qiymatlar
sohasini toping.
68.
A) (−2; +∞)
B) (−1; +∞)
tengsizlikni yeching.
C) [−1; +∞)
D) (0; +∞)
A) (3; 3 ) ∪ (3 ; 4)
2𝑥−3 3𝑥+1 = 15
62. Agar
<0
1
1
3
3
1
B) (2;3) ∪{3 }
3
1
1
C) (3; 3 )
D) (2; 3 )
3
tenglamaning ildizi a bo’lsa,
𝑥0 −
√10−3𝑥
𝑙𝑜𝑔2 |𝑥−3|
D) 12
3
69. Agar
1
𝑙𝑔6
lg(𝑥 + 3) − 𝑙𝑔
1
=1
𝑥
ni toping.
bo’lsa, x ni toping.
A) 𝑙𝑜𝑔6 12 B) 3𝑙𝑜𝑔6 2 C) 2𝑙𝑜𝑔6 2 D) 𝑙𝑜𝑔6 2
A) 2
63. |𝑥 − 7|𝑙𝑜𝑔2 (𝑥 − 2) = 3(𝑥 − 7)
70. 828𝑥+5 = √16𝑥+100 tenglamani yeching.
1
B) 17
8
C) 17
1
D) 19
8
C) -5
D) -2
5
tenglamaning ildizlari yig’indisini toping.
A) 9
B) 5
A) 10
1
8
B) 9
C) 11
D) 12
71. Tenglamalar sistemasini yeching:
23𝑥 + 3𝑦 = 4
{ 𝑥+1
3
− 2𝑦 = 6
𝑙𝑜𝑔 (𝑥 − 4)2 ≤ 2
64. { 2
(𝑥 − 1)2 > 4
1
2
tengsizliklar sistemasi nechta butun yechimga
A) (𝑙𝑜𝑔3 4; )
B) (𝑙𝑜𝑔3 2; )
ega?
C) (𝑙𝑜𝑔3 2; 0)
D) (0; 𝑙𝑜𝑔3 2)
A) cheksiz ko’p
B) 2 ta
C) 3 ta
D) butun yechimga ega emas
72. 8
65. Ushbu
4
−1
=1
2
2𝑥 −4𝑥+4 − 1
agar u bitta bo’lsa) 12 dan qanchaga kam?
C) 6
D) 10
66. Agar 𝑙𝑜𝑔2 𝑎 = 2, (3) va 𝑙𝑜𝑔2 𝑏 = 3, (6)
bo’lsa, a · b + 1 ning qiymatini toping.
B)25,9+1
A) 33
D)21,3+1
C) 65
𝑥
3√𝑥+2
1
2
B) 6
C) 5
2
− 9𝑥 =
63√𝑥+2
− 54
tenglamaning ildizlari kvadratlarining
yig’indisini toping.
D) 4
73. 𝑙𝑜𝑔22 𝑥 + 2 ≥ 3𝑙𝑜𝑔2 𝑥
tengsizlikni yeching.
A) (0; 2] ∪ [4; ∞)
1
1
4
2
B) [2; 4]
D) (−∞; 2] ∪ [4; ∞)
C) (0; ] ∪ [ ; ∞)
4
74. √4𝑥+1 =
8𝑥 4𝑥−1
√2
tenglamani yeching.
67. Ushbu
2
<
tengsizlikning eng kichik natural yechimini
A) 3
tenglamaning ildizlari yig’indisi (yoki ildizi,
B) 8
𝑥2
3
5−
3
toping
𝑥 2 −5𝑥+6
A) 4
3
A)
1
3
C)−
B)
5
6
2
3
D)54
2𝑙𝑜𝑔0,01(𝑥 2 +1)
75. (√3)
=
1
33^𝑙𝑜𝑔0,01 (𝑥 2 +1)
tenglamaning eng katta ildizini toping.
A)3√11
C)2√2
76. 𝑓(𝑥) =
B) ildizga ega emas
D)3
3𝑥−1 +3𝑥−2 +3𝑥−3
5𝑥−2 +145𝑥
funksiya berilgan bo’lsa, 9·f (−2) ni hisoblang.
A) 25
B) 1,44
C) 9
D) 0,36