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LOGARITMA

LOGARITMA. Pengertian Logaritma. P log a = m artinya a = p m Keterangan: p disebut bilangan pokok a disebut bilangan logaritma atau numerus dengan a > 0 m disebut hasil logaritma atau eksponen dari basis. Logaritma dengan basis 10.

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LOGARITMA

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  1. LOGARITMA

  2. Pengertian Logaritma Plog 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

  3. Logaritma dengan basis 10 • Pada bentuk plog a = m, maka: 10log a = m cukup ditulis log a = m. • Basis 10 pada logaritma tidak perlu dituliskan. • Contoh: 10log 3  dituliskan log 3 10log 5  dituliskan log 5

  4. m m = plog (a) n n 4. plog plog a = 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

  5. Contoh Soal

  6. Contoh Soal 1. Jika 2log x = 3 Tentukan nilai x = …. Jawab: 2log x = 3  x = 23 x = 8.

  7. Contoh Soal 2. Jika 4log 64 = x Tentukan nilai x = …. Jawab: 4log 64 = x  4x = 64 4x = 44 x = 4.

  8. Contoh Soal 3. Nilai dari 2log 8 + 3log 9 = …. Jawab: = 2log 8 + 3log 9 = 2log 23 + 3log 32 = 3 + 2 = 5

  9. Contoh Soal 4. Nilai dari 2log (8 x 16) = …. Jawab: = 2log 8 + 2log 16 = 2log 23 + 2log 24 = 3 + 4 = 7

  10. Contoh Soal 5. Nilai dari 3log (81 : 27) = …. Jawab: = 3log 81 - 3log 27 = 3log 34 - 3log 33 = 4 - 3 = 1

  11. Contoh Soal 6. Nilai dari 2log 84 = …. Jawab: = 2log 84 = 4 x 2log 23 = 4 x 3 = 12

  12. 2log 8 = 4 2 Contoh Soal 7. Nilai dari 2log 84 = …. Jawab: = 2log 84 = 2 x 2log 23 = 2 x 3 = 6

  13. Contoh Soal 8. Jika log 100 = x Tentukan nilai x = …. Jawab: log 100 = x  10x = 100 10x = 102 x = 2.

  14. Latihan Soal

  15. 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

  16. 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

  17. Jawaban log 3 = 0,477 dan log 2 = 0,301 Nilai log 18 = …. a. 1,552 b. 1,525 c. 1,255 d. 1,235 c. 1,255

  18. 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

  19. 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

  20. Jawaban log 2 = 0,301 dan log 5 = 0,699 Nilai log 5 + log 8 + log 25 = …. a. 2 b. 3 c. 4 d. 5 b. 3

  21. 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

  22. 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

  23. Jawaban Diketahui log 4,72 = 0,674 Nilai dari log 4.720 = …. a. 1,674 b. 2,674 c. 3,674 d. 4,674 c. 3,674

  24. 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

  25. 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

  26. Jawaban 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 d. 2,130

  27. 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

  28. 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

  29. Jawaban Diketahui log 3 = a dan log 2 = b. Maka log 18 = …. a. 2a – b b. 2a + b c. a + 2b d. a – 2b b. 2a + b

  30. Soal - 6 Diketahui plog 27 = 3x Maka plog 243 = …. a. 4x b. 5x c. 6x d. 7x

  31. Pembahasan plog 27 = 3x 33 = p3x Maka: x = 1 dan p = 3 plog 243 = 3log (3)5 = 5.3log 3 = 5 . X = 5x

  32. Jawaban Diketahui plog 27 = 3x Maka plog 243 = …. a. 4x b. 5x c. 6x d. 7x b. 5x

  33. Soal - 7 Diketahui log 2 = 0,301 Maka log 50 = …. a. 0,699 b. 1,301 c. 1,699 d. 2,301

  34. Pembahasan log 2 = 0,301 log 50 = log (100 : 2) = log 100 – log 2 = log 102 – log 2 = 2 – 0,301 = 1,699

  35. Jawaban Diketahui log 2 = 0,301 Maka log 50 = …. a. 0,699 b. 1,301 c. 1,699 d. 2,301 c. 1,699

  36. Terima Kasih.. Jangan Lewatkan Program Khusus Pembahasan Soal-soal UN 2001 s.d. 2005

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