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Clase 126

Clase 126. Ejercicios sobre inecuaciones logarítmicas. x 2 + x. log 5 < log 5 x. x + 2. x 2 + x. < x. x 2 + x. x + 2. – x < 0. x + 2. Estudio individual de la clase anterior. b) log 5 (x 2 +x) – log 5 (x + 2) < log 5 x. x 2 + x – x(x + 2). < 0. x + 2.

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Clase 126

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  1. Clase 126 Ejercicios sobre inecuaciones logarítmicas

  2. x2+ x log5 < log5x x + 2 x2+ x < x x2+ x x + 2 – x < 0 x + 2 Estudio individual de la clase anterior b) log5(x2+x) – log5(x + 2) < log5x

  3. x2+ x – x(x + 2) < 0 x + 2 x2+ x – x2 – 2x < 0 x + 2 – x < 0 x + 2 x > 0 x + 2 0 –2 –1 x2+ x > 0 x(x+1) > 0 ceros x1 = 0 ; x3 = –1 C.N. x1 = 0 x + 2 > 0 x > –2 C.D. x2 = –2 x > 0 + +

  4. c) log (7x2 – 3)  2 (x2+1) Ejercicio Resuelve las siguientes inecuaciones a) log2(x – 5) + log2(x – 4) < 1 b) log4(2x + 1) – log4x > log43 d) log2(x+5)+log2(x+3) < log2(x+9) e) log2(x – 7) – log2(x2 – 4)  1

  5. 6 3 5 4 a) log2(x – 5) + log2(x – 4) < 1 log2 [(x – 5)(x – 4)]< 1 ceros: x1= 3 ; x2= 6 log2 (x2 – 9x + 20)< 1 x2 – 9x + 20 < 2 x2 – 9x + 18 < 0 x > 5 (x – 3)(x – 6) < 0 x > 4 5 < x < 6 + +

  6. 2x + 1 · (– 1) > 3 x 2x + 1 x x – 1 < 0 x b) log4(2x + 1) – log4x > log43 2x + 1 log4 > log43 x – 3 > 0 2x + 1 – 3x > 0 x –x + 1 > 0 x

  7. 1 x – 1 x > – < 0 2 x 1 0 1 – 2 x > 0 C.N. x1= 1 C.D. x2= 0 + + 0 < x < 1

  8. c) log (7x2 – 3)  2 (x2+1) x2+1 > 0 x * 7x2 – 3  (x2+1)2 7x2 – 3  x4+2x2 +1 0  x4–5x2 + 4 x4–5x2 + 4 0 (x2 – 4)(x2 – 1) 0 (x + 2)(x – 2)(x + 1)(x – 1) 0 ceros: x1;2=  2 ; x3;4= 1

  9. 3 x2 > 7  3 x >   7 ceros: x1;2=  2 ; x3;4= 1 7x2 – 3 > 0 7x2 > 3 x >  0,65 x < – 0,65 ó x > 0,65

  10. 2 1 0 –1 –2 ceros: x1;2=  2 ; x3;4= 1 x < – 0,65 ó x > 0,65 x  –2 ó –1 x < – 0,65 ó 0,65 < x  1 ó x  2 + + + 0,65 – 0,65

  11. Para el estudio individual Incisos d y e del ejercicio de la clase Respuestas: d) – 3 < x < – 1 e) x > 7

  12. d) log2(x+5)+log2(x+3) < log2(x+9) log2 [(x + 5)(x + 3)]< log2(x+9) [(x + 5)(x + 3)]< x + 9 x2 + 8x + 15 < x + 9 x2 + 7x + 6 < 0 (x + 6)(x + 1) < 0 Ceros: x1 = –6 ; x2 = –1

  13. –1 –6 –3 –9 –5 Ceros: x1 = –6 ; x2 = –1 x > –3 x > –5 x > –9 – 3 < x < – 1 + +

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