1. 25log5x − 52log2𝑥 = 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. 42𝑙𝑔x + 112𝑙𝑔x = 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. 733x+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 +145x 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 = 42 √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. 82 = 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: 392x + 29x − 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 (1643(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 28𝑙𝑜𝑔7 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 12𝑙𝑜𝑔4 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. 73𝑥+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 − 32𝑥+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. 828𝑥+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: 23𝑥 + 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 = 63√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 33^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 +145𝑥 funksiya berilgan bo’lsa, 9·f (−2) ni hisoblang. A) 25 B) 1,44 C) 9 D) 0,36