Pembahasan-logaritma Kelas x

PEMBAHASAN LOGARITMA by Nur Laila Indah Sari,S.Si MATEMATIKANET.COM

PEMBAHASAN 1. Jawab : D Ingat :

log ൌ ՞ ൌ ௡ log 25 = 2 ՞ 25 ൌ 5ଶ

a

5

2. Jawab : A Ingat : a

log ൌ ՞ ൌ ௡ log 32 = 2p ՞ 32 = 2ଶ௣

2

3. Jawab : A Ingat :

log ൌ ՞ ൌ ௡ ଵ ଵ 7 = ՞ log = -2 ସଽ ସଽ

a

-2

7

4. Jawab : E 2

2

2

2

log 4 + log 10 – log 5 = log

ൈସଵ଴ ହ

2

= log 8 2

= log 2

3

2

= 3 log 2 = 3

ൈ1=3

5. Jawab : B 2

2

ସ଼ ଷ

2

log 48 – log 3 = log 2

= log 16 2

= log

2ସ

2

= 4 log 2 = 4

ൈ1=4

6. Jawab : C 5

5

5

log 50 – log 2 = log

ହ଴ ଶ

5

= log 25 5

= log 5

5ଶ

= 2 log 5 = 2

ൈ1=2

7. Jawab : E 8

ሺ64௫ ൈ 4ሻ = 3 െ

log

1

ሺ64௫ ൈ 4ሻ = log 8ଷି௫ 64௫ ൈ 4 = 8ଷି௫ య 2଺௫ ൈ 2ଶ ൌ ଼଼ೣ 2଺௫ ൈ 2ଶ ൈ 8௫ ൌ 8ଷ 2଺௫ ൈ 2ଶ ൈ 2ଷ௫ ൌ 2ଽ 2ଽ௫ାଶ ൌ 2ଽ 9 ൅2=9 9 ൌ7 ൌ ଻ଽ 8

8

log

8. Jawab : B 6

6

3

log 15 = log 3 . log 15

ଵ

=

3

ଵ

=

3

3

log3.2

3

. log 3 + log 5

ଵ

= =

log6

3

. log 3 . 5

3

.

log3 + 3 log 2

ሺ1 ൅ ሻ

ଵା௕ ଵା௕ ሺଵା௕ሻ௔ = ௔ାଵ ଵାೌభ = ೌశభ ೌ

9. Jawab : D 3

5

3

5

3

3

5

5

log 36 + log 100 – log 4 – log 4 = log 36 – log 4 + log 100 – log 4 3

= log

ଷ଺ 5 ଵ଴଴ ସ + log ସ

3

5

= log 9 + log 25 3

2

5

2

= log 3 + log 5 =2+2=4 10. Jawab : A b3

log

ଶ = ଶ .blog a ଷ ଶ ଵ ଶ = . ൌ ଷ ௣ ଷ௣

11. Jawab : E  x

2 = 18 2

2

2

2

log 18 = log 2.9 = log 2 + log 9 2

2

2

= log 2 + log 3

2

2

= 1 + 2 log 3 12. Jawab : D 4

4

3

log 15 = log 3 + log 15

ଵ

=

3

3

log4

. log 3.5

ଵ3 3 ௕ log 3 + log 5 ଵ ଵ = ቀ1 ൅ ቁ ௕ ௔ ቀଵାೌభቁ ௔ାଵ ௔ାଵ = = = ௕ ௔ ௔௕ =

13. Jawab : C 3

3

log 27 + log

√ 3 =

3

log

3ଷ +

3

3

భ

log మ

ଵ ଶ

3

3

= 3. log 3 + . log 3 = 3 +

ଵ ଵ =3 ଶ ଶ

14. Jawab : A log 75 = log

ଷ଴଴ ସ

= log 300 – log 4 = log 100.3 – log

2ଶ

= log 100 + log 3 – 2.log 2 = 2 + 0.4771 – 2.0,3010 = 2,4771 – 0,602 = 1,8751

15. Jawab : A log

ଵ଴௫య ଷ ଶ ௬మ = log 10 െ log = log 10 + log ଷ െ log ଶ

െ 2.log =1൅3 െ2 = 1 + 3.log

16. Jawab : E 2

log 25

ൈ

3

log 8

ൈ

5

5ଶ ൈ log 2ଷ ൈ log 3ଶ = 2. log 5 ൈ 3. log 2 ൈ 2. log 3 2

3

log 9 = log 2

5

3

2

5

5

3

= 2.3.2. log 5. log 3. log 2 2

= 12. log 2 = 12

17. Jawab : E 3

2 2

ሺ2 െ 6ሻ = 3 log ሺ2 െ 6ሻ = log 2 2 െ6=2 2 െ6=8 2 =8+6 2 ൌ 14 log

2

3

3

=

ଵସ ଶ =7

18. Jawab : A 12

12

log 3 +

12

log 4 = =

log 3.4

12

log 12 = 1

19. Jawab : B 5

log 4

ൈ

2

log 3

ൈ

9

ൈ log 3 ൈ log 5 ଵ = 2. log 2 ൈ log 3 ൈ log 5 ଶ ଵ = 2. . log 2 ൈ log 3 ൈ log 5 ଶ 5

log 5 = log 2 5

2

32

2

2

5

3

2

3

5

= 1 . log 5 = 1 20. Jawab : D log 6 = log 2.3 = log 2 + log 3 = 0,3010 + 0,4771 = 0,7781 21. Jawab : A 2

2

6

log 64 = log 2 = 6

22. Jawab : E 2

log

ଵ ଵଶ଼

2

-7

= log 2 = -7

23. Jawab : D 2

2

log 256 = log 16 = log 16 = 2

ൈ 1,20412 = 2,40824

24. Jawab : C 2

log 3 =

୪୭୥ଷ ଴,ସ଻଻ଵ ୪୭୥ଶ = ଴,ଷ଴ଵ଴ = 1,58505

25. Jawab : D 16

log 5 =

24

log 3 =

ଵ 2 ସ . log 5 = 4

2

2

log 5 =

2

4 2

2

log 25 = log 5 = 2. log 5 =

2.4 = 8

5