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Assalamu’alaikum wr. wb

Assalamu’alaikum wr. wb. LOGARITMA. Pengertian Logaritma. Logaritma sebagai invers dari eksponen. Contoh : 2³ = n, maka n = 8, ini permasalahan pangkat 2ˣ = 8, maka nilai x = 3, ini permasalahan logaritma dapat ditulis ²log 8 = x ⇔ ²log 8 = 3 3² = b, maka b = 9, ini permasalah eksponen

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Assalamu’alaikum wr. wb

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  1. Assalamu’alaikum wr. wb

  2. LOGARITMA

  3. Pengertian Logaritma Logaritma sebagai invers dari eksponen. Contoh : • 2³ = n, maka n = 8, ini permasalahan pangkat 2ˣ = 8, maka nilai x = 3, ini permasalahan logaritma dapat ditulis ²log 8 = x ⇔ ²log 8 = 3 • 3² = b, maka b = 9, ini permasalah eksponen 3ˣ = 9, maka x = 2, ini permasalahan logaritma dapat ditulis ³log 9 = x ⇔³log 9 = 2

  4. Logaritma Biasa Logaritma Secara umum ditulis, • a disebut bilangan pokok logaritma atau basis • b dsebut yang dilogaritmakan • c disebut hasil logaritma • a > 0, a = 1, b > 0 • bilangan pokok 10 boleh tidak ditulis

  5. Sifat-sifat Logaritma • ᵖlog (axb) = ᵖlog a + ᵖlog b

  6. g. h. • ᴾlog 1 = 0 • ᴾlog p = 1

  7. ᴾlog a . ᵃlog b = ᴾlog b dengan a > 0, b > 0, p ≠ 1 dan p > 0 ᵖlog 1 = 0ᵖlog p = 1 persamaan logaritma ⇔ ᵃlog b = c b = aᶜ

  8. Contoh • ²log 32 = ²log 2⁵ = 5 x ²log 2 = 5 • ⁵log = ⁵log 10 - ⁵log 2 • ²log 8 = ²log 2³ = 3 . ²log 2 = 3 . 1 = 3 • ²log 3 = • = ⁸log 2 • .

  9. ³ log 1 = 0 • ² log 2 = 1 contoh persamaan logaritma ³log (2x – 1) + ³log x = 0 ³log ((2x – 1)(x) = ³ log 1 ³log (2x² - x ) = ³log 1 (2x² - x) = 1 (2x² - x - 1) = 0 (2x + 1 )(x – 1) = 0 2x = -1 x = atau x = 1

  10. Contoh Soal Selesaikan soal berikut: • ³log 81 + ³log 243 - ³log 27 • ³log 27 - ³ log 81 • ⁵log 125 carilah himpunan persamaan logaritma ⁹log (2x – 1) =

  11. Penyelesaian • ³log 81 + ³log 243 - ³log 27 = ³log ( ) = ³log 729 = ³log 3⁶ = 6 . 1 = 1

  12. ³log 27 - ³ log 81 = ³log ( ) = ³log ( ) = ³log = -1³log 3 = -1 • ⁵log 125 = ⁵log 5³ = 3⁵log 5 = 3 . 1 = 3

  13. ⁹log (2x – 1) = ⇔⁹log (2x – 1) = ⁹log ⇔(2x – 1) = ⇔ 2x – 1 = ⇔ 2x – 1 = 3 ⇔ x = 2

  14. Wassalamu’alaikum wr. Wb

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