Esercizi da fare su equazion sito Matematika
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(2) Equazioni logaritmiche. Logaritmi. 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39. 𝑙𝑙𝑙𝑙𝑙𝑙1 (𝑥𝑥 − 2) = 0 2. 𝑙𝑙𝑙𝑙𝑙𝑙4 (3𝑥𝑥 − 4) = − 𝑥𝑥 − 2 = −2 3 2. 𝑙𝑙𝑙𝑙𝑙𝑙3. 𝑥𝑥 = 3. 3 2. 𝑥𝑥 = 𝑥𝑥 =. 𝑙𝑙𝑙𝑙𝑙𝑙𝑥𝑥 4 = 1. −1 < 𝑥𝑥 < 0 ∪ 𝑥𝑥 > 0. 𝑙𝑙𝑙𝑙𝑙𝑙𝑥𝑥−2 9 = 2. 𝑥𝑥 = 5. 𝑙𝑙𝑙𝑙𝑙𝑙1 −2 = 2 𝑙𝑙𝑙𝑙𝑙𝑙3−2𝑥𝑥. 𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖. 1 = −2 3. 𝑙𝑙𝑙𝑙𝑙𝑙2 (𝑥𝑥 + 1) + 𝑙𝑙𝑙𝑙𝑙𝑙2 3 = 𝑙𝑙𝑙𝑙𝑙𝑙2 (𝑥𝑥 − 1) 𝑙𝑙𝑙𝑙𝑙𝑙3 (3𝑥𝑥 + 1) − 𝑙𝑙𝑙𝑙𝑙𝑙3 𝑥𝑥 = 2. 2 𝑙𝑙𝑙𝑙𝑙𝑙2 (𝑥𝑥 + 2) + 𝑙𝑙𝑙𝑙𝑙𝑙1 𝑥𝑥 + 1 = 0 1 𝑙𝑙𝑙𝑙𝑙𝑙3 𝑥𝑥 2 + 2 = − 𝑙𝑙𝑙𝑙𝑙𝑙1 2 2 3. 41. v 3.0. 𝑥𝑥 =. 1 6. 𝑥𝑥 = −2. 3. 2 9. 1+√2 𝑥𝑥 = �. 2. 𝑙𝑙𝑙𝑙𝑙𝑙2 (𝑥𝑥 − 2) − 𝑙𝑙𝑙𝑙𝑙𝑙4 (3𝑥𝑥 − 1) = 1. 2. 𝑥𝑥 = 8 + 2√14. 1 2 𝑙𝑙𝑙𝑙𝑙𝑙1 � 𝑥𝑥 − 1� = 2 − 𝑙𝑙𝑙𝑙𝑙𝑙9 𝑥𝑥 4 3 3. 𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖. 3𝑥𝑥 − 1 =2 𝑥𝑥. 𝑥𝑥 = −. 𝑙𝑙𝑙𝑙𝑙𝑙1 𝑙𝑙𝑙𝑙𝑙𝑙2 (3𝑥𝑥 − 1) = 0. 𝑥𝑥 = 1. 𝑙𝑙𝑙𝑙𝑙𝑙2 𝑙𝑙𝑙𝑙(𝑥𝑥 + 1) = 1 − 𝑙𝑙𝑙𝑙𝑙𝑙4 3. equazioni logaritmiche risolubili mediante una posizione. 40. 3 − √3 2. 𝑥𝑥 = ±. 3 𝑙𝑙𝑙𝑙𝑙𝑙1 𝑥𝑥 − 2 = 𝑙𝑙𝑙𝑙𝑙𝑙2 (𝑥𝑥 3 − 1). 3. 𝑥𝑥 =. 𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖. 2. 𝑙𝑙𝑙𝑙𝑙𝑙2 𝑙𝑙𝑙𝑙𝑙𝑙3. 10 3. 𝑥𝑥 = 4. 𝑙𝑙𝑙𝑙𝑙𝑙𝑥𝑥+1 1 = 0. 𝑥𝑥. 11 8. 2 𝑙𝑙𝑙𝑙𝑙𝑙2 𝑥𝑥 + 5 𝑙𝑙𝑙𝑙𝑙𝑙 𝑥𝑥 − 3 = 0. 1 78. 2. 𝑥𝑥 = 𝑒𝑒 √3 − 1 𝑥𝑥 = 10−3 ∪ 𝑥𝑥 = √10. 𝑙𝑙𝑙𝑙𝑙𝑙2 2 𝑥𝑥 − 4 𝑙𝑙𝑙𝑙𝑙𝑙2 𝑥𝑥 + 4 = 0. 𝑥𝑥 = 4. © 2016 - www.matematika.it. 2 di 7.
(3) Equazioni logaritmiche. Logaritmi. 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62. v 3.0. 3 𝑙𝑙𝑙𝑙𝑙𝑙2 𝑥𝑥 + 𝑙𝑙𝑙𝑙𝑙𝑙 𝑥𝑥 = −4. 𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖. 3 𝑙𝑙𝑙𝑙𝑙𝑙2 𝑥𝑥 + 5 𝑙𝑙𝑙𝑙𝑙𝑙 𝑥𝑥 = 0. 𝑥𝑥 = 1 ∪ 𝑥𝑥 = 10−3. 2 𝑙𝑙𝑙𝑙𝑙𝑙2 𝑥𝑥 + 3 = 7 𝑙𝑙𝑙𝑙𝑙𝑙 𝑥𝑥. 𝑥𝑥 = 103 ∪ 𝑥𝑥 = √10 5. 𝑙𝑙𝑙𝑙𝑙𝑙32 𝑥𝑥 + 𝑙𝑙𝑙𝑙𝑙𝑙3 𝑥𝑥 − 12 = 0. 𝑥𝑥 = 27 𝑥𝑥 =. −2𝑙𝑙𝑙𝑙2 𝑥𝑥 + 𝑙𝑙𝑙𝑙𝑙𝑙 + 1 = 0. 𝑥𝑥 = 𝑒𝑒 𝑥𝑥 =. 𝑙𝑙𝑙𝑙3 𝑥𝑥 − 9𝑙𝑙𝑙𝑙𝑙𝑙 = 0. 𝑙𝑙𝑙𝑙𝑙𝑙 𝑥𝑥 (𝑙𝑙𝑙𝑙𝑙𝑙 𝑥𝑥 + 1) + 5 𝑙𝑙𝑙𝑙𝑙𝑙 𝑥𝑥 = 𝑙𝑙𝑙𝑙𝑙𝑙2 𝑥𝑥 + 4 𝑙𝑙𝑙𝑙𝑙𝑙 𝑥𝑥 − 7 𝑙𝑙𝑙𝑙𝑙𝑙2 2 𝑥𝑥 + 95 = 8√6 𝑙𝑙𝑙𝑙𝑙𝑙2 𝑥𝑥 3(𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 + 1) = 5 𝑙𝑙𝑙𝑙𝑙𝑙2 𝑥𝑥. 𝑥𝑥 = 𝑒𝑒. √𝑒𝑒. 7. 𝑥𝑥 = 10−2. 𝑥𝑥 = 2 4√6−1 ∪ 𝑥𝑥 = 2 4√6+1 3−√69 10. 𝑥𝑥 = 10. 2 =5 𝑙𝑙𝑙𝑙𝑙𝑙2 (𝑥𝑥 + 3). 3+√69 10. ∪ 𝑥𝑥 = 10. 𝑥𝑥 = √2 − 3 ∪ 𝑥𝑥 = 1. 1 2 + =2 𝑙𝑙𝑙𝑙𝑙𝑙 𝑥𝑥 𝑙𝑙𝑙𝑙𝑙𝑙 𝑥𝑥 + 1. 𝑥𝑥 = 10 ∪ 𝑥𝑥 = √10/10. 𝑙𝑙𝑙𝑙 𝑥𝑥 + 1 =1 𝑙𝑙𝑛𝑛2 𝑥𝑥 + 1. 𝑥𝑥 = 1 ∪ 𝑥𝑥 = 𝑒𝑒. (𝑙𝑙𝑙𝑙𝑙𝑙 𝑥𝑥 − 3)(𝑙𝑙𝑙𝑙𝑙𝑙 𝑥𝑥 + 3) = 0. 𝑥𝑥 = 103 ∪ 𝑥𝑥 = 10−3. 𝑙𝑙𝑙𝑙𝑙𝑙5 𝑥𝑥 − 𝑙𝑙𝑙𝑙𝑙𝑙25 𝑥𝑥 = 1. 𝑥𝑥 = 25. 3 3 1 + =− 𝑙𝑙𝑙𝑙𝑙𝑙4 𝑥𝑥 2 + 𝑙𝑙𝑙𝑙𝑙𝑙4 𝑥𝑥 𝑙𝑙𝑙𝑙𝑙𝑙4 𝑥𝑥 + 1. 𝑥𝑥 = 2. 4 − 2 𝑙𝑙𝑙𝑙𝑙𝑙4 𝑥𝑥 5 + 3 𝑙𝑙𝑙𝑙𝑙𝑙4 𝑥𝑥 = 𝑙𝑙𝑙𝑙𝑙𝑙4 𝑥𝑥 3 𝑙𝑙𝑙𝑙𝑙𝑙4 𝑥𝑥 + 5. −2√7±2 √7 4. 𝑥𝑥 = 43. 𝑙𝑙𝑙𝑙𝑙𝑙22 𝑥𝑥 − 4 𝑙𝑙𝑙𝑙𝑙𝑙2 𝑥𝑥 + 3 = 0. 𝑥𝑥 = 2 ∪ 𝑥𝑥 = 8. 2𝑙𝑙𝑙𝑙2 (𝑥𝑥 − 1) − 5 𝑙𝑙𝑙𝑙(𝑥𝑥 − 1) + 2 = 0. 𝑥𝑥 = √𝑒𝑒 + 1 𝑥𝑥 = 𝑒𝑒 2 + 1. 𝑙𝑙𝑙𝑙𝑙𝑙32 (𝑥𝑥 + 2) − 𝑙𝑙𝑙𝑙𝑙𝑙3 (𝑥𝑥 + 2) − 2 = 0. 𝑥𝑥 = −. 3𝑙𝑙𝑙𝑙𝑙𝑙12 𝑥𝑥 − 11𝑙𝑙𝑙𝑙𝑙𝑙1 𝑥𝑥 − 4 = 0 2. 1. 𝑥𝑥 = 1 𝑥𝑥 = 𝑒𝑒 3 𝑥𝑥 = 𝑒𝑒 −3. 𝑙𝑙𝑙𝑙2 𝑥𝑥 − 2 𝑙𝑙𝑙𝑙 𝑥𝑥 + 1 = 0. 2 𝑙𝑙𝑙𝑙𝑙𝑙2 (𝑥𝑥 + 3) +. 1 81. 3. 5 ∪ 𝑥𝑥 = 7 3. 𝑥𝑥 = √2 𝑥𝑥 =. 2. © 2016 - www.matematika.it. 1 16. 3 di 7.
(4) Equazioni logaritmiche. Logaritmi. 63 64 65 66 67. 𝑙𝑙𝑙𝑙2 (𝑥𝑥 2 − 1) + 3𝑙𝑙𝑙𝑙(𝑥𝑥 2 − 1) = 0. 𝑥𝑥 = ±�1 +. 𝑙𝑙𝑙𝑙𝑙𝑙32 (𝑥𝑥 − 2) + 𝑙𝑙𝑙𝑙𝑙𝑙1 (𝑥𝑥 − 2) = 6. 𝑥𝑥 =. 𝑙𝑙𝑙𝑙𝑙𝑙22 𝑥𝑥 − 𝑙𝑙𝑙𝑙𝑙𝑙2 𝑥𝑥 3 + 2 = 0. 𝑥𝑥 = 2 ∪ 𝑥𝑥 = 4. 3. 𝑙𝑙𝑙𝑙𝑙𝑙22 (2𝑥𝑥 + 1) − 𝑙𝑙𝑙𝑙𝑙𝑙1 (2𝑥𝑥 + 1) = 0 2 𝑙𝑙𝑙𝑙𝑙𝑙𝑥𝑥−1 3 − 𝑙𝑙𝑙𝑙𝑙𝑙𝑥𝑥−1 3 − 2 = 0. 𝑥𝑥 =. 𝑙𝑙𝑙𝑙𝑙𝑙24 (2𝑥𝑥 − 3) − 5𝑙𝑙𝑙𝑙𝑙𝑙22 (2𝑥𝑥 − 3) + 4 = 0. 69. 2𝑙𝑙𝑙𝑙𝑙𝑙42 𝑥𝑥(𝑥𝑥 − 1) + 𝑙𝑙𝑙𝑙𝑙𝑙1 [𝑥𝑥(𝑥𝑥 − 1)]7 + 3 = 0. 71 72 73 74 75. 4. 2 𝑙𝑙𝑙𝑙𝑙𝑙2𝑥𝑥+1 27 + 𝑙𝑙𝑙𝑙𝑙𝑙2𝑥𝑥+1 1�27 − 6 = 0. 𝑙𝑙𝑙𝑙𝑙𝑙2 (𝑥𝑥 − 4) − 3 =. 2 𝑙𝑙𝑙𝑙𝑙𝑙1 (𝑥𝑥 − 4) 2. − 𝑙𝑙𝑙𝑙𝑙𝑙1 (2𝑥𝑥 + 5) (𝑙𝑙𝑙𝑙𝑙𝑙3 (2𝑥𝑥 + 5) − 1) = 2 3. (𝑙𝑙𝑙𝑙𝑙𝑙2 (3𝑥𝑥 + 4) − 1)2 = 𝑙𝑙𝑙𝑙𝑙𝑙2 2 2. 𝑙𝑙𝑙𝑙𝑙𝑙3 2𝑥𝑥 2 (𝑙𝑙𝑙𝑙𝑙𝑙3 2𝑥𝑥 2 − 1) = 𝑙𝑙𝑙𝑙𝑙𝑙3 2𝑥𝑥 2 + 3. 77. 𝑙𝑙𝑙𝑙𝑙𝑙2 (𝑥𝑥 − 3)2 (𝑙𝑙𝑙𝑙𝑙𝑙2 (𝑥𝑥 − 3) − 2) − 𝑙𝑙𝑙𝑙𝑙𝑙1 (𝑥𝑥 − 3) = 2 2. 𝑙𝑙𝑙𝑙𝑙𝑙32 (2𝑥𝑥 2 − 𝑥𝑥) = 1 equazioni logaritmiche con argomento esponenziale. 79 v 3.0. 𝑥𝑥 = −1 ∪ 𝑥𝑥 = 2 ∪ 𝑥𝑥 =. 1 ± √257 2. 𝑥𝑥 = −. 26 81. √3 − 9 18. 𝑥𝑥 = 6 ∪ 𝑥𝑥 = 8 𝑥𝑥 = −. 7 ∪ 𝑥𝑥 = 2 3. 𝑥𝑥 = −1 ∪ 𝑥𝑥 = 0 ∪ 𝑥𝑥 = −. 76. 78. 5 7 ∪ 𝑥𝑥 = 2 2 7 13 ∪ 𝑥𝑥 = ∪ 𝑥𝑥 = 4 8 𝑥𝑥 =. 𝑥𝑥 = −2 ± √5. 𝑙𝑙𝑙𝑙𝑙𝑙12 [𝑥𝑥(𝑥𝑥 + 4)] = 𝑙𝑙𝑙𝑙𝑙𝑙1 [𝑥𝑥(𝑥𝑥 + 4)] 2. 1 4. 4 ∪ 𝑥𝑥 = 1 + √3 3. 𝑥𝑥 = 1 ∪ 𝑥𝑥 =. 𝑙𝑙𝑙𝑙𝑙𝑙12 (3𝑥𝑥 + 1) + 𝑙𝑙𝑙𝑙𝑙𝑙3 (3𝑥𝑥 + 1)6 = −9 3. 19 ∪ 𝑥𝑥 = 29 9. 𝑥𝑥 = 0 ∪ 𝑥𝑥 = −. 2. 68. 70. 1 ∪ 𝑥𝑥 = ±√2 𝑒𝑒 3. 𝑙𝑙𝑙𝑙 2𝑥𝑥 = 0. 4 ± 3√2 2. 27 𝑥𝑥 = ±� 2. ∪ 𝑥𝑥 = ±�. 1 6. 𝑥𝑥 = 7 ∪ 𝑥𝑥 =. 1. √2. 3 2 3 ± √33 ∪ 𝑥𝑥 = 12. 𝑥𝑥 = −1 ∪ 𝑥𝑥 =. +3. 𝑥𝑥 = 0 © 2016 - www.matematika.it. 4 di 7.
(5) Equazioni logaritmiche. Logaritmi. 80 81 82 83 84 85 86 87 88 89. 𝑙𝑙𝑙𝑙𝑙𝑙5 7𝑥𝑥 = 1. 𝑙𝑙𝑙𝑙𝑙𝑙5 2𝑥𝑥 −1 =. 𝑥𝑥 = 𝑙𝑙𝑙𝑙𝑙𝑙7 5. 1 4. 𝑥𝑥 = 1 +. 𝑙𝑙𝑙𝑙(1 − 𝑒𝑒 𝑥𝑥 ) = 0. 𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖. 1 − 𝑙𝑙𝑙𝑙𝑙𝑙 3𝑥𝑥 = 𝑙𝑙𝑙𝑙𝑙𝑙 2𝑥𝑥. 𝑥𝑥 =. 𝑙𝑙𝑙𝑙𝑙𝑙(3𝑥𝑥 + 1) + 𝑙𝑙𝑙𝑙𝑙𝑙(3𝑥𝑥 − 1) = 2. 𝑥𝑥 𝑙𝑙𝑙𝑙𝑙𝑙2 3 + 𝑙𝑙𝑙𝑙𝑙𝑙2 5𝑥𝑥 = (2𝑥𝑥 − 1) 𝑙𝑙𝑙𝑙𝑙𝑙2 5 − 𝑥𝑥 𝑙𝑙𝑙𝑙𝑙𝑙2 5 𝑙𝑙𝑙𝑙(22𝑥𝑥 − 9 ∙ 2𝑥𝑥 + 21) = 0. 𝑙𝑙𝑙𝑙𝑙𝑙2 (4𝑥𝑥 + 2𝑥𝑥 ) − 𝑙𝑙𝑙𝑙𝑙𝑙2 2 = 0 𝑙𝑙𝑙𝑙 4𝑥𝑥. 2 −6. 1 4 𝑙𝑙𝑙𝑙𝑙𝑙5 2. 𝑙𝑙𝑙𝑙 10 𝑙𝑙𝑙𝑙 6. 1 𝑥𝑥 = 𝑙𝑙𝑙𝑙𝑙𝑙3 101 2 𝑥𝑥 = −. 𝑙𝑙𝑙𝑙 5 𝑙𝑙𝑙𝑙 3. 𝑥𝑥 = 2 ∪ 𝑥𝑥 = 𝑥𝑥 = 0. − 𝑙𝑙𝑙𝑙 64 = 0. 𝑙𝑙𝑙𝑙𝑙𝑙2 (2𝑥𝑥 + 1) + 𝑙𝑙𝑙𝑙𝑙𝑙2 2 (2𝑥𝑥 + 1) − 2 = 0. 𝑙𝑙𝑙𝑙 5 𝑙𝑙𝑙𝑙 2. 𝑥𝑥 = ±3 𝑥𝑥 = 0. equazioni logaritmiche di riepilogo 90 91 92 93 94 95 96 97 98 99. v 3.0. 𝑙𝑙𝑙𝑙𝑙𝑙4 (𝑥𝑥 2 + 2) − 𝑙𝑙𝑙𝑙𝑙𝑙4 (𝑥𝑥 2 − 1) = 𝑙𝑙𝑙𝑙𝑙𝑙4 5 − 𝑙𝑙𝑙𝑙𝑙𝑙4 (𝑥𝑥 + 1). 𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖. (𝑙𝑙𝑙𝑙𝑙𝑙2 𝑥𝑥 2 )2 +9 𝑙𝑙𝑙𝑙𝑙𝑙2 𝑥𝑥 + 2 = 0. 1 1 𝑥𝑥 = , 𝑥𝑥 = 4 4 √2. 𝑥𝑥 √2 𝑙𝑙𝑙𝑙𝑙𝑙(10 − 𝑥𝑥 2 ) − 𝑙𝑙𝑙𝑙𝑙𝑙 8 = 2 𝑙𝑙𝑙𝑙𝑙𝑙 − 2 𝑙𝑙𝑙𝑙𝑙𝑙 5 5 𝑙𝑙𝑙𝑙𝑙𝑙(𝑥𝑥 − 1) − 2 ∙ 𝑙𝑙𝑙𝑙𝑙𝑙(𝑥𝑥 + 1) − 𝑙𝑙𝑙𝑙𝑙𝑙 8 = −2 3 2 + =2 𝑙𝑙𝑙𝑙𝑙𝑙2 𝑥𝑥 − 1 𝑙𝑙𝑙𝑙𝑙𝑙2 𝑥𝑥 + 1 𝑙𝑙𝑙𝑙𝑙𝑙2 3𝑥𝑥 − 2 = 0 𝑥𝑥−1 2. 𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 𝑥𝑥 = 8, 𝑥𝑥 = 𝑥𝑥 =. 2 𝑙𝑙𝑙𝑙𝑙𝑙3 4𝑥𝑥 = 𝑙𝑙𝑙𝑙𝑙𝑙1 2−𝑥𝑥 𝑙𝑙𝑙𝑙 2. 𝑥𝑥 = √2. 𝑙𝑙𝑙𝑙 4 𝑙𝑙𝑙𝑙 3. 𝑥𝑥 = 0. 3. 𝑥𝑥 = 1 +. −1=0. 3 1 𝑙𝑙𝑙𝑙 2𝑥𝑥 +1 − 2 𝑙𝑙𝑙𝑙 = 1 2 2. √2 2. 2 𝑙𝑙𝑙𝑙 2. 1 2 𝑥𝑥 = � − 7� 3 𝑙𝑙𝑙𝑙 2. −2 𝐿𝐿𝐿𝐿𝐿𝐿 42−𝑥𝑥 + 5 𝐿𝐿𝐿𝐿𝐿𝐿 2𝑥𝑥+1 = 1. 𝑥𝑥 = 𝑙𝑙𝑙𝑙𝑙𝑙512 80 © 2016 - www.matematika.it. 5 di 7.
(6) Equazioni logaritmiche. Logaritmi. 100 101 102 103 104 105 106. 𝑥𝑥−1. 2 𝑙𝑙𝑙𝑙 33𝑥𝑥+1 = 𝑙𝑙𝑙𝑙 9. 𝑥𝑥 = −1. 𝑥𝑥 𝑙𝑙𝑙𝑙𝑙𝑙2 3 − 𝑙𝑙𝑙𝑙𝑙𝑙4 9 = 0. 𝑥𝑥 = 1. − 𝑙𝑙𝑙𝑙 2𝑥𝑥 + 2 𝑙𝑙𝑙𝑙 3 = 1 − 𝑙𝑙𝑙𝑙 4−𝑥𝑥 (2𝑥𝑥 − 1) 𝑙𝑙𝑙𝑙𝑙𝑙7 2 = 1 + 𝑥𝑥 𝑙𝑙𝑙𝑙𝑙𝑙1 4 (𝑥𝑥 + 1) 𝑙𝑙𝑙𝑙 3 − 𝑙𝑙𝑙𝑙. 7. 1 1 𝑥𝑥 = 2 𝑙𝑙𝑙𝑙 � � 9 3. 𝑥𝑥 =. 𝑙𝑙𝑙𝑙 9 − 1 𝑙𝑙𝑙𝑙 8. 𝑥𝑥 =. 𝑙𝑙𝑙𝑙 14 𝑙𝑙𝑙𝑙 16. 𝑥𝑥 = −1. 1 𝑙𝑙𝑙𝑙 2 + 4 𝑙𝑙𝑙𝑙𝑙𝑙2 𝑒𝑒 = 0 𝑥𝑥. 𝑥𝑥 = −ln2 √2. 𝑙𝑙𝑙𝑙 3𝑥𝑥 + 2 𝑙𝑙𝑙𝑙𝑙𝑙3𝑥𝑥 𝑒𝑒 − 3 = 0. 𝑥𝑥 =. 1 2 ∪ 𝑥𝑥 = 𝑙𝑙𝑙𝑙 3 𝑙𝑙𝑙𝑙 3. 𝑙𝑙𝑙𝑙 10 𝑙𝑙𝑙𝑙 2 𝑙𝑙𝑙𝑙 10 ∪ 𝑥𝑥 = 3 𝑙𝑙𝑙𝑙 2. 𝑥𝑥 = −. 107. 𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥 2 − 3 𝑙𝑙𝑙𝑙𝑙𝑙2𝑥𝑥 10 − 2 = 0. 108. 2 − 3𝑥𝑥 𝑙𝑙𝑙𝑙𝑙𝑙4 3𝑥𝑥 + 2(𝑙𝑙𝑙𝑙𝑙𝑙4 9 − 𝑙𝑙𝑙𝑙𝑙𝑙4 4) = 0. 2 𝑥𝑥 = ± √3 3. 𝐿𝐿𝐿𝐿𝐿𝐿(24𝑥𝑥 − 1) + 2 𝐿𝐿𝐿𝐿𝐿𝐿 3 = (1 − 2𝑥𝑥) 𝐿𝐿𝐿𝐿𝐿𝐿 4. 4 𝑥𝑥 = 𝑙𝑙𝑙𝑙𝑙𝑙16 � � 3. 109 110 111 112 113 114 115 116 117 118 119 120 v 3.0. �(𝑥𝑥 + 1) 𝐿𝐿𝐿𝐿𝐿𝐿 3 − 1�(1 + 𝐿𝐿𝐿𝐿𝐿𝐿 3𝑥𝑥 +1 ) = 0 3 − 𝑥𝑥 + 𝑙𝑙𝑙𝑙𝑙𝑙2 32𝑥𝑥+1 = 0 3. 𝑙𝑙𝑙𝑙𝑙𝑙3 �9𝑥𝑥+2 − 2� = 𝑥𝑥 + 1. 𝑥𝑥 = −1 ±. 𝑥𝑥 = −. 1 𝐿𝐿𝐿𝐿𝐿𝐿 3. 𝑙𝑙𝑙𝑙 24 𝑙𝑙𝑙𝑙 9 − 𝑙𝑙𝑙𝑙 2. 𝑥𝑥 = −1. 𝑙𝑙𝑙𝑙|3𝑥𝑥 − 1| = 𝑥𝑥𝑥𝑥𝑥𝑥 9. 𝐿𝐿𝐿𝐿𝐿𝐿(4𝑥𝑥 − 1) + 𝐿𝐿𝐿𝐿𝐿𝐿 2 = 𝐿𝐿𝐿𝐿𝐿𝐿(22𝑥𝑥 + 3 ∙ 2𝑥𝑥+1 − 10) 𝑙𝑙𝑙𝑙𝑙𝑙 5 − 𝑙𝑙𝑙𝑙𝑙𝑙(2𝑥𝑥 − 3) = 1. (2 𝑙𝑙𝑙𝑙𝑙𝑙 𝑥𝑥 − 5) 𝑙𝑙𝑙𝑙𝑙𝑙 𝑥𝑥 = 3 − 𝑙𝑙𝑙𝑙𝑙𝑙 𝑥𝑥. 𝑥𝑥 = 𝑙𝑙𝑙𝑙𝑙𝑙3 � 𝑥𝑥 = 2 𝑥𝑥 =. 7 4. 𝑥𝑥 = 10. 𝑙𝑙𝑙𝑙𝑙𝑙(𝑒𝑒 𝑥𝑥 + 1) = 𝑙𝑙𝑙𝑙𝑙𝑙(𝑒𝑒 2𝑥𝑥 − 1). 𝑙𝑙𝑙𝑙𝑙𝑙 5 + (𝑥𝑥 − 2) 𝑙𝑙𝑙𝑙𝑙𝑙 4 = 𝑙𝑙𝑙𝑙𝑙𝑙(4𝑥𝑥 − 11) 1 3 1 + = 2 2 𝑙𝑙𝑙𝑙𝑙𝑙2 𝑥𝑥 − 2 𝑙𝑙𝑙𝑙𝑙𝑙2 𝑥𝑥 − 1 4. 𝑙𝑙𝑙𝑙𝑙𝑙 𝑥𝑥 − 2 𝑙𝑙𝑙𝑙𝑙𝑙 𝑥𝑥 − 2 𝑙𝑙𝑙𝑙𝑙𝑙2 𝑥𝑥 − 4 + = 𝑙𝑙𝑙𝑙𝑙𝑙 𝑥𝑥 − 1 𝑙𝑙𝑙𝑙𝑙𝑙 𝑥𝑥 − 3 (𝑙𝑙𝑙𝑙𝑙𝑙 𝑥𝑥 − 3)(1 − 𝑙𝑙𝑙𝑙𝑙𝑙 𝑥𝑥). © 2016 - www.matematika.it. 2−√10 2. √5 − 1 � 2. ∪ 𝑥𝑥 = 10. 2+√2 2. 𝑥𝑥 = ln 2 𝑥𝑥 = 2 𝑥𝑥 =. 1 ∪ 𝑥𝑥 = 32 8. 2. 𝑥𝑥 = 102 ∪ 𝑥𝑥 = 103 6 di 7.
(7) Equazioni logaritmiche. Logaritmi. 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140. v 3.0. 𝑙𝑙𝑙𝑙𝑙𝑙2 (2𝑥𝑥 − 1) 𝑙𝑙𝑙𝑙𝑙𝑙2 (2𝑥𝑥+1 − 2) = 0. 𝑥𝑥 = 1 ∪ 𝑥𝑥 = log 2. 𝑙𝑙𝑙𝑙𝑙𝑙3 �𝑥𝑥 2 − 𝑥𝑥 = 𝑙𝑙𝑙𝑙𝑙𝑙3 √2. 𝑥𝑥 = −1 ∪ 𝑥𝑥 = 2. 𝑙𝑙𝑙𝑙(𝑒𝑒 2𝑥𝑥 − 1) = 𝑙𝑙𝑙𝑙(1 − 𝑒𝑒 𝑥𝑥 ). 𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖. 𝑙𝑙𝑙𝑙𝑙𝑙3 (2𝑥𝑥 − 1) + 𝑙𝑙𝑙𝑙𝑙𝑙1 (𝑥𝑥 − 4) = −1. 𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖. 3. 𝑙𝑙𝑙𝑙𝑙𝑙1 (𝑥𝑥 − 1) − 𝑙𝑙𝑙𝑙𝑙𝑙2 (𝑥𝑥 + 1) = 3. 𝑥𝑥 =. 2. 𝑙𝑙𝑙𝑙𝑙𝑙(32𝑥𝑥 + 2) + 𝑙𝑙𝑙𝑙𝑙𝑙 1 (3𝑥𝑥 − 2) = 1 10. 1 1 𝑙𝑙𝑙𝑙(𝑥𝑥 − 1) + 𝑙𝑙𝑙𝑙 √3 = [𝑙𝑙𝑙𝑙(5𝑥𝑥 2 − 20) − 𝑙𝑙𝑙𝑙(𝑥𝑥 − 2)] 2 2 𝑙𝑙𝑙𝑙𝑙𝑙�51+√𝑥𝑥 + 51−√𝑥𝑥 � = 1 𝑙𝑙𝑙𝑙�√3𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 + 𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐� = 0. 𝑥𝑥. =. 𝑥𝑥 𝑥𝑥 = 1. 3√2 4. 𝑥𝑥 = log 3 5 + √3 𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 𝑥𝑥 = 0 𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖. 2𝑥𝑥 2 𝑙𝑙𝑙𝑙 𝑥𝑥 + 5𝑥𝑥 𝑙𝑙𝑙𝑙 𝑥𝑥 − 3 = 0 𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐. 3 2. 𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖. 𝜋𝜋 𝑥𝑥 = 1 ∪ 𝑥𝑥 = ± + 2𝑘𝑘𝑘𝑘 6. √3 𝑥𝑥 2. 𝑥𝑥 = 1. 𝑙𝑙𝑙𝑙𝑙𝑙𝑥𝑥 𝑥𝑥 = 0. 𝑥𝑥 = 1. 𝑥𝑥 𝑥𝑥 = 𝑥𝑥 3−𝑥𝑥. 𝑙𝑙𝑙𝑙𝑙𝑙2 (3 − 2𝑥𝑥) − 2 𝑙𝑙𝑙𝑙𝑙𝑙1 𝑥𝑥 = 0 𝑙𝑙𝑙𝑙𝑙𝑙32 (3𝑥𝑥 − 1) − 𝑙𝑙𝑙𝑙𝑙𝑙1 (3𝑥𝑥 − 1)4 + 3 = 0 3. 𝑥𝑥 − 𝑙𝑙𝑙𝑙𝑙𝑙4 3𝑥𝑥 = 1 2 1 1 � 𝑙𝑙𝑙𝑙 2𝑥𝑥 − 𝑙𝑙𝑙𝑙 3� � − 4� = 0 2 𝑙𝑙𝑙𝑙 𝑥𝑥 𝑙𝑙𝑙𝑙𝑙𝑙2. 3 ∪ 𝑥𝑥 = 1 2. 𝑥𝑥 =. 1 𝑙𝑙𝑙𝑙 3. 𝑥𝑥 = 1. 2. 𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥 3 = 1. 𝑥𝑥 =. 𝑥𝑥 =. 𝑥𝑥 = 48 𝑥𝑥 =. 𝑙𝑙𝑙𝑙𝑙𝑙𝑥𝑥 3 = 2 𝑙𝑙𝑙𝑙𝑙𝑙1 +1 √3. 𝑥𝑥 =. 𝑥𝑥. © 2016 - www.matematika.it. 4 28 ∪ 𝑥𝑥 = 9 81 9 4 ∪ 𝑥𝑥 = √𝑒𝑒 2 1 + √5 2. 7 di 7.
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