Logaritmos con cambio de base

Presentación del tema: "Logaritmos con cambio de base"— Transcripción de la presentación:

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2 Logaritmos con cambio de base
Profesor Moisés Grillo Ing. Industrial Derechos reservados Prohibida su reproducción

3 𝑙𝑜𝑔 32 8

4 = 3 5 𝑙𝑜𝑔 32 8 =𝑙𝑜𝑔 8 2 32 2 4 2 16 2 8 2 2 2 4 2 1 2 2 1

5 = 4 3 𝑙𝑜𝑔 27 81 =𝑙𝑜𝑔 81 3 27 3 27 3 9 3 3 3 9 3 1 3 3 1

6 = 2 3 = 1 5 𝑙𝑜𝑔 8 4 = 𝑙𝑜𝑔 𝑙𝑜𝑔 32 2 = 𝑙𝑜𝑔 3 = 6 4 = 3 2 = 2 3 𝑙𝑜𝑔 16 64 = 𝑙𝑜𝑔 𝑙𝑜𝑔 = 𝑙𝑜𝑔 2 = 1 4 = 1 3 𝑙𝑜𝑔 81 3 = 𝑙𝑜𝑔 𝑙𝑜𝑔 27 3 = 𝑙𝑜𝑔 = 1 2 = 3 5 𝑙𝑜𝑔 32 8 𝑙𝑜𝑔 49 7 = 𝑙𝑜𝑔 = 𝑙𝑜𝑔

7 𝑙𝑜𝑔 𝑛 𝑎 𝑏 = 𝑙𝑜𝑔 𝑛 𝑎− 𝑙𝑜𝑔 𝑛 𝑏 = 𝑙𝑜𝑔 2 1 2 2 𝑙𝑜𝑔 2 3 2 𝑙𝑜𝑔 3 2 1 4
= 𝑙𝑜𝑔 𝑙𝑜𝑔 𝑙𝑜𝑔 = 𝑙𝑜𝑔 Cambio de Base 𝑙𝑜𝑔 𝑥 1=0 𝑙𝑜𝑔 𝑎 𝑎 𝑛 =𝑛 𝑙𝑜𝑔 𝑙𝑜𝑔 = 𝑙𝑜𝑔 2 1− 𝑙𝑜𝑔 𝑙𝑜𝑔 2 2 = −2 1 3 1 =− 6 1 =−6 𝑙𝑜𝑔 𝑏 𝑛 𝑎 = 1 𝑛 𝑙𝑜𝑔 𝑏 𝑎 𝑙𝑜𝑔 𝑛 𝑎 𝑏 = 𝑙𝑜𝑔 𝑛 𝑎− 𝑙𝑜𝑔 𝑛 𝑏

8 𝑙𝑜𝑔 𝑛 𝑎 𝑏 = 𝑙𝑜𝑔 𝑛 𝑎− 𝑙𝑜𝑔 𝑛 𝑏 = 𝑙𝑜𝑔 3 5 3 𝑙𝑜𝑔 3 1 3 4 𝑙𝑜𝑔 1 81 5 3
= 𝑙𝑜𝑔 𝑙𝑜𝑔 𝑙𝑜𝑔 = 𝑙𝑜𝑔 𝑙𝑜𝑔 𝑏 𝑛 𝑎 = 1 𝑛 𝑙𝑜𝑔 𝑏 𝑎 Cambio de Base = 𝑙𝑜𝑔 3 3 𝑙𝑜𝑔 3 1− 𝑙𝑜𝑔 = −4 𝑙𝑜𝑔 𝑙𝑜𝑔 =− 1 20 1 𝑙𝑜𝑔 𝑎 𝑎 𝑛 =𝑛 𝑙𝑜𝑔 𝑥 1=0 𝑙𝑜𝑔 𝑛 𝑎 𝑏 = 𝑙𝑜𝑔 𝑛 𝑎− 𝑙𝑜𝑔 𝑛 𝑏

9 = 𝑙𝑜𝑔 𝑙𝑜𝑔 𝑙𝑜𝑔 = 𝑙𝑜𝑔 = − 𝑙𝑜𝑔 𝑙𝑜𝑔 2 2 =− 9 2 = 𝑙𝑜𝑔 𝑙𝑜𝑔 = 𝑙𝑜𝑔 5 5 𝑙𝑜𝑔 5 1− 𝑙𝑜𝑔 5 5 = −1 =− 1 2 𝑙𝑜𝑔 = 𝑙𝑜𝑔 𝑙𝑜𝑔 𝑙𝑜𝑔 = 𝑙𝑜𝑔 = − 𝑙𝑜𝑔 𝑙𝑜𝑔 3 3 =−8 1 = 𝑙𝑜𝑔 𝑙𝑜𝑔 = 𝑙𝑜𝑔 2 2 − 𝑙𝑜𝑔 = −4 𝑙𝑜𝑔 = 𝑙𝑜𝑔 =− 1 10 1 2

10 𝑙𝑜𝑔 = 𝑙𝑜𝑔 Cambio de Base = 𝑙𝑜𝑔 𝑙𝑜𝑔

11 𝑙𝑜𝑔 𝑙𝑜𝑔 1 2 𝑙𝑜𝑔 𝑙𝑜𝑔 − 𝑙𝑜𝑔 𝑙𝑜𝑔 2 2+ 𝑙𝑜𝑔 2 2 𝑙𝑜𝑔 𝑙𝑜𝑔 − 𝑙𝑜𝑔 2 2 𝑙𝑜𝑔 2 2 𝑙𝑜𝑔 2 2− 1 3 = = 3 4 − 1 3 = 12+9−2 6 = 19 6

12 𝑙𝑜𝑔 = 𝑙𝑜𝑔 = 𝑙𝑜𝑔 𝑙𝑜𝑔 = = 3 2

13 𝑙𝑜𝑔 5 7 3 7 7 3 7 7 Cambio de Base = 𝑙𝑜𝑔 7 3 7 7 𝑙𝑜𝑔 7 5 7 3 7 7
= 𝑙𝑜𝑔 𝑙𝑜𝑔 𝑙𝑜𝑔 = 𝑙𝑜𝑔 𝑙𝑜𝑔 = 5 𝑙𝑜𝑔 𝑙𝑜𝑔 Cambio de Base = 5 𝑙𝑜𝑔 7 7+ 𝑙𝑜𝑔 𝑙𝑜𝑔 7 7+ 𝑙𝑜𝑔 − 𝑙𝑜𝑔 7 7 = − 1 2 = −3 6 = = = 15 5 =3 1 2

14 𝑙𝑜𝑔 ∙ 𝑙𝑜𝑔 ∙ = 62 45 = 7 66 𝑙𝑜𝑔 𝑙𝑜𝑔 = 28 75 = 15 14 𝑙𝑜𝑔 ∙ 𝑙𝑜𝑔 ∙ = 25 63 = 11 45