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Logaritma

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  • 1. Pengertian Logaritma log a = m artinya a = pm Keterangan: p disebut bilangan pokok a disebut bilangan logaritma atau numerus dengan a > 0 m disebut hasil logaritma atau eksponen dari basis P
  • 2. Logaritma dengan basis 10    Pada bentuk plog a = m, maka: 10 log a = m cukup ditulis log a = m. Basis 10 pada logaritma tidak perlu dituliskan. Contoh: 10 log 3  dituliskan log 3 10 log 5  dituliskan log 5
  • 3. Sifat-sifat Logaritma 1. plog (a x b) = plog a + plog b 2. plog (a : b) = plog a - plog b 3. plog (a)n = n x plog a 4. log n am = plog (a) p = m n m n log a p
  • 4. Contoh Soal 1. Jika 2log x = 3 Tentukan nilai x = …. Jawab: 2 log x = 3  x = 23 x = 8.
  • 5. Contoh Soal 2. Jika 4log 64 = x Tentukan nilai x = …. Jawab: 4 log 64 = x  4x = 64 4x = 4 4 x = 4.
  • 6. Contoh Soal 3. Nilai dari 2log 8 + 3log 9 = …. Jawab: = 2log 8 + 3log 9 = 2log 23 + 3log 32 = 3+2 = 5
  • 7. Contoh Soal 4. Nilai dari 2log (8 x 16) = …. Jawab: = 2log 8 + 2log 16 = 2log 23 + 2log 24 = 3+4 = 7
  • 8. Contoh Soal 5. Nilai dari 3log (81 : 27) = …. Jawab: = 3log 81 - 3log 27 = 3log 34 - 3log 33 = 4-3 = 1
  • 9. Contoh Soal 6. Nilai dari 2log 84 = …. Jawab: = 2log 84 = 4 x 2log 23 =4x3 = 12
  • 10. Contoh Soal 7. Nilai dari 2log √84 = …. Jawab: = 2log √84  = = 2 x 2log 23 =2x3 =6 4 2 log 8 2
  • 11. Contoh Soal 8. Jika log 100 = x Tentukan nilai x = …. Jawab: log 100 = x  10x = 100 10x = 102 x = 2.
  • 12. Soal - 1 log 3 = 0,477 dan log 2 = 0,301 Nilai log 18 = …. a. 1,552 b. 1,525 c. 1,255 d. 1,235
  • 13. Pembahasan log 3 = 0,477 dan log 2 = 0,301 log 18 = log 9 x 2 = log 9 + log 2 = log 32 + log 2 = 2 (0,477) + 0,301 = 0,954 + 0,301 = 1,255
  • 14. Jawaban log 3 = 0,477 dan log 2 = 0,301 Nilai log 18 = …. a. 1,552 b. 1,525 c. 1,255 c. 1,255 d. 1,235
  • 15. Soal - 2 log 2 = 0,301 dan log 5 = 0,699 Nilai log 5 + log 8 + log 25 = …. a. 2 b. 3 c. 4 d. 5
  • 16. Pembahasan log 2 = 0,301 dan log 5 = 0,699 = log 5 + log 8 + log 25 = log 5 + log 23 + log 52 = log 5 + 3.log 2 + 2.log 5 = 0,699 + 3(0,301) + 2(0,699) = 0,699 + 0,903 + 1,398 = 3,0
  • 17. Jawaban log 2 = 0,301 dan log 5 = 0,699 Nilai log 5 + log 8 + log 25 = …. a. 2 b. 3 b. 3 c. 4 d. 5
  • 18. Soal - 3 Diketahui log 4,72 = 0,674 Nilai dari log 4.720 = …. a. 1,674 b. 2,674 c. 3,674 d. 4,674
  • 19. Pembahasan log 4,72 = 0,674 log 4.720 = log (4,72 x 1000) = log 4,72 + log 1000 = log 4,72 + log 103 = 0,674 + 3 = 3,674
  • 20. Jawaban Diketahui log 4,72 = 0,674 Nilai dari log 4.720 = …. a. 1,674 b. 2,674 c. 3,674 c. 3,674 d. 4,674
  • 21. Soal - 4 Diketahui log 3 = 0,477 dan log 5 = 0,699. Nilai log 135 = …. a. 2,778 b. 2,732 c. 2,176 d. 2,130
  • 22. Pembahasan log 3 = 0,477 dan log 5 = 0,699. log 135 = log (27 x 5) = log 27 + log 5 = log 33 + log 5 = 3(0,477) + 0,699 = 1,431 + 0,699 = 2,130
  • 23. Jawaban Diketahui log 3 = 0,477 dan log 5 = 0,699. Nilai log 135 = …. a. 2,778 b. 2,732 d. 2,130 c. 2,176 d. 2,130
  • 24. Soal - 5 Diketahui log 3 = a dan log 2 = b. Maka log 18 = …. a. 2a – b b. 2a + b c. a + 2b d. a – 2b
  • 25. Pembahasan Diketahui log 3 = a dan log 2 = b. log 18 = log (9 x 2) = log 9 + log 2 = log 32 + log 2 = 2.log 3 + log b = 2(a) + b = 2a + b
  • 26. Jawaban Diketahui log 3 = a dan log 2 = b. Maka log 18 = …. a. 2a – b b. 2a + b b. 2a + b c. a + 2b d. a – 2b
  • 27. Soal - 6 Diketahui plog 27 = 3x Maka plog 243 = …. a. 4x b. 5x c. 6x d. 7x
  • 28. Pembahasan log 27 = 3x 33 = p3x Maka: x = 1 dan p = 3 p log 243 = 3log (3)5 = 5.3log 3 = 5.X = 5x p
  • 29. Jawaban Diketahui plog 27 = 3x Maka plog 243 = …. a. 4x b. 5x b. 5x c. 6x d. 7x
  • 30. Soal - 7 Diketahui log 2 = 0,301 Maka log 50 = …. a. 0,699 b. 1,301 c. 1,699 d. 2,301
  • 31. Pembahasan log 2 = 0,301 log 50 = log (100 : 2) = log 100 – log 2 = log 102 – log 2 = 2 – 0,301 = 1,699
  • 32. Jawaban Diketahui log 2 = 0,301 Maka log 50 = …. a. 0,699 b. 1,301 c. 1,699 c. 1,699 d. 2,301
  • 33. Jangan Lewatkan Program Khusus Pembahasan Soal-soal UN 2001 s.d. 2005

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