TALLER DE LOGARITMOS

1. Expresar en forma exponencial:

1 . log3 9= 2 2 . log6 36 = 2 3 . log214

=−2

4 . log3127

=−3 5. log16 8 = 34

6 . log 27 81 = 43

7 . log14

(18 ) =32

8 . log827

(49 ) =23

9. log916

(24332 )= 52

10 . loga13

a2 = 6 11. loga2a6 = 3 12 . log

a3a2 = 2

3

2. Expresar en forma logarítmica:

1 . 72 = 49 2 . 34 = 81 3 . 25 = 32

4 . 2512 = 5 5 . 16

14 = 2 6 . 27

23 = 9

7 . 2−4 = 116

8 . 3−2 = 19

9. (18 )−13 = 2

10 . (127 )−23 = 9 11. (916 )−

12 =43

12 . (1681 )−34= 27

8

3. Hallar los valores de los logaritmos siguientes:1 . log 64 2 . log4 16 3 . log2 644 . log225 15 5. log421 11 6 . log144 12

7 . log243 3 8 . logb6b4 9 . log

b35

b6

4. Hallar los valores de a y b en los ejercicios siguientes:1 . logb a = 3 2. log4 a = 4 3 . log2 b = 8

4 . loga 125 =3 5 . loga 27 = 3 6 . loga 9 =12

7 . logb 3 = 14

8 . logb 27= 34

9 . loga 16 = 45

5. Efectuar y expresar en forma más simple:

1 . log 2 − log3 +log 5

2 . 3 log 2− 4 log 3 + 12

(log 25 ) − 13

( log 64 ) + 23

(log 27 )

3 . log 32 + 3 log 24 −4 log 3√8 − 3 log 3√125 + log 3√7294 .12 ( log5 25 ) − 1

3 ( log2 64 ) + 23 ( log3 27 ) + log 7516 −2 log 59

+ log23243

5 . log10 13 + log10 7 + log10 2 −2 log10 3

6 . loga (x2+1 )12 + loga ( x+4 ) − (32 ) loga (x2−1 )

7 .12loga (2 x+1 ) + 3

4 [loga (3 x−1 ) ] − 12 [ loga (2x−1 ) ]