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LOGARITMA

LOGARITMA. a log b = x  b = a x. Ingat:. Ingat:. Eksponen/pangkat. 5 3 = 125. basis/bilangan pokok. 4 x = 64 x= ?. Logaritma: x = 4 log 64. Pengertian Logaritma. Logaritma merupakan invers /kebalikan dari perpangkatan /eksponen. a log b = x  b = a x Keterangan:

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LOGARITMA

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  1. LOGARITMA alog b = xb = ax

  2. Ingat:

  3. Ingat: Eksponen/pangkat 53 = 125 basis/bilangan pokok 4x = 64 x= ? Logaritma: x = 4log 64

  4. Pengertian Logaritma Logaritma merupakan invers/kebalikan dari perpangkatan/eksponen. alog b = xb = ax Keterangan: a disebut bilangan pokok/basis, a > 0, a≠ 1 b disebut bilangan logaritma atau numerus dengan,b>0 x disebut hasil logaritma atau eksponen dari basis

  5. Logaritma basis 10 Basis 10 pada logaritma tidak perlu dituliskan. Contoh: 10log 3  dituliskan log 3 10log 5  dituliskan log 5

  6. Contoh: • Nyatakan bentuk eksponen berikut menjadi bentuk logaritma: • 34 = 81 • 23 = 8 Jawab: Ingat: alog b = xb = ax

  7. Nyatakan bentuk logaritma berikut menjadi bentuk eksponen: a. 5log 25 = 2 • 2log 32 = 5 Jawab: Ingat: alog b = xb = ax

  8. Sifat-sifat Logaritma: 1. alog a = 1 2. alog 1 = 0 3. alogb + alogc = alog (b.c) 4. alogb – alogc = 5. alogbn = n . alogb 6. alogb = 7. alogb . blog c = alogc 8.amlogbn = 9. aalogb = b Catatan: ( alog b)2 = alog2b =(alog b)(alog b)

  9. Contoh: 1. Jika 2log x = 3 Tentukan nilai x = …. Jawab: 2. Nilai dari 2log (8 . 16) = …. Jawab: alog b = xb = ax alogb + alogc = alog (b.c) alogbn = n . alogb aloga =1

  10. 3.Nilaidari3log (81 : 27) = …. Jawab: 4. Nilaidari2log 84 = …. Jawab: alogb-alogc = alogbn = n . alogb aloga =1 alogbn = n . alogb aloga =1

  11. 5. Nilaidari2log 8 + 3log 9 = …. Jawab: = 2log 8 + 3log 9 = 2log 23 + 3log 32 =3. 2log 2 + 2.3log 3 = 3 + 2 = 5 Hati-hati! Basisnya berbeda! alogbn = n . alogb aloga =1

  12. 5. Nilaidari2log 8 + 3log 9 = …. Jawab: Hati-hati! Basisnya berbeda! alogbn = n . alogb aloga =1

  13. 6. Jika= . . . Jawab: alogbn=

  14. 7. Nilai dari Jawab: alogbn = n . alogb aloga =1

  15. Nilai dari (6log 9 + 2.6log 2) - 2. 6log 6 = . . . Jawab: alogb + alogc = alog (b.c) alogbn = n . alogb aloga =1

  16. 9. Nilai dari2log 125x 5log 4= . . . Jawab: alogbn = n . alogb alogb . blog c = alogc aloga =1

  17. 10. Nilai dari125log 25 = . . . Jawab: amlogbn =

  18. 11. Tentukan nilai ! Jawab: alog b alogb + alogc = alog (b.c)

  19. 12.Tentukan nilai dari 22log 9! Jawab: 13.Tentukan nilai dari 82log 5! Jawab: aalogb = b

  20. 14.Tentukan nilai dari ! Jawab: alogb . blog c = alogc alogb + alogc = alog (b.c) alogbn = n . alogb alogb . blog c = alogc

  21. 15.Tentukan nilai dari ! Jawab: alogbn = n . alogb aalogb = b

  22. 16. Jika 3log 4= a dan 4log 5 = b maka 12log 15 adalah … .

  23. 17. Jika 2log 3= p dan 3log 5 = q maka 15log 45 adalah … .

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