Muhammad Zainal Abidin | admin of http:meetabied.wordpress.com

  http://meetabied.wordpress.com Matematika X – Semester 1 | SMAN 1 Bone-Bone Hasil yang paling berharga dari semua jenis pendidikan adalah kemampuan untuk membuat diri kita melakukan sesuatu yang harus kita lakukan, pada saat hal itu harus dilakukan, baik kita menyukainya maupun tidak. Ini adalah pelajaran pertama yang harus dipelajari, dan semua apa pun seseorang mulai belajar, pelajaran ini mungkin pelajaran terakhir yang sungguh-sungguh dapat ia kuasai. (Thomas Huxley)

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BAB I BENTUK PANGKAT, AKAR, DAN LOGARITMA ] Bentuk Logaritma | Sifat-sifat Logaritma

  ================================================================================ Materi ini dapat disebarluaskan secara bebas, untuk tujuan bukan komersial, dengan atau tanpa menyertakan sumber. Hak Cipta selamanya pada Allah Swt. J Salam hangat selalu … Muhammad Zainal Abidin | admin of http://meetabied.wordpress.com

Bab I Bentuk Pangkat, Akar, dan Logaritma Standar Kompetensi : 1. Memecahkan masalah yang berkaitan dengan bentuk pangkat, akar, dan Logaritma Kompetensi Dasar: 1. Menggunakan aturan pangkat, akar, dan logaritma 2. Melakukan manipulasi aljabar dalam perhitungan yang melibatkan pangkat, akar, dan

  Sifat-sifat logaritma 1.

  . ^a log b 8. ^a log 1 = 0 9. ^a log a ⁿ = n

  n m

  log log 6. ^a log b x ^b log c = ^a log c 7. ^{n a} log b ^m =

  a b _c ^c

  = ^a log b - ^a log c 4. ^a log b ⁿ = n ^a log b 5. ^a log b =

  c b

  ç è æ

  ÷ ø ö

  b ^{b a} = ^log 2. ^a log (b x c)= ^a log b + ^a log c 3. ^a log

  a

  logaritma

  Alokasi Waktu:

   Logaritma

  Pertemuan ke-10 s.d. 13

Rangkuman Materi

C.

  6. Siswa dapat merasionalkan bentuk akar.

  5. Siswa dapat menyederhanakan bentuk aljabar yang memuat pangkat rasional dan logaritma.

  4. Siswa dapat melakukan operasi aljabar pada bentuk pangkat, akar, dan logaritma.

  3. Siswa dapat mengubah bentuk pangkat ke bentuk logaritma, dan sebaliknya.

  2. Siswa dapat mengubah bentuk akar ke bentuk pangkat,dan sebaliknya.

  Siswa dapat mengubah bentuk pangkat negatif ke pangkat positf, dan sebaliknya.

  Indikator Pencapaian Hasil Belajar 1.

  26 jam pelajaran (13 x pertemuan)

  Logaritma adalah operasi invers dari perpangkatan. Jika a ^x = b, maka ditulis dalam bentuk logaritma ^a log b = x. Dibaca logaritma b dengan basis a adalah x. a disebut bilangan pokok/basis untuk a > 0 dan a ¹ 1, x disebut numerik x > 0

  Catatan : ₁₀ Logaritma dengan bilangan pokok 10, yakni log x, sering ditulis log x.

  Contoh: ₂

  1 ₂

  1 ₂ 1. ! log log log

  24 Sederhanakan

  4

3 Jawab:

  ₂

  1 ₂

  1 _{2 2}

  1

  1

  x x

  log log log + + 24 = log( 24 )

  4

  3 ₂

  4

  3 = log

  2

  = 1 2. Sederhanakan! _{2 log 3} a.

  2 ₂ b.

  98

  log c.

  log 150 + log 2 – log 3 Jawab: _{2 log 3}

  a. =3

  2 _{2 2}

  b. log 98 = log (49. 2) ₂ = log ( 7. 7. 2) _{2 2 2}

  = log 7 + log 7 + log 2 ₂ = 2 log 7 + 1 150 .

  2 æ ö c.

  Log 150 + log 2 – log 3 = log ç ÷

  3 è ø

  = log 100 = 2 _{5 5}

  3. log 3 = p tentukan log 75! Jika

  Jawab: _{5 5} log 75 = log(3 x 5) _{5 5} = log 3 + log 25 _{5 2}

  = p + log 5 = p + 2

  Latihan Kerjakan soal-soal di bawah ini dengan benar ! 1.

  Nyatakan menjadi bentuk pangkat ! ₂

  1

  1

  a. log ₃ 2 = -

  1

  b. log = -4 ₂₅

  81

  1

  c. log 0,2 = -

  2

  5

  d. log 1 = 0 Jawab: ₂

  1

  1

  a. log

  2 = -

  2

  2

  ×××× 2 = …. ₃

  1

  b. log = -4

  81

  ×××× 3 =….. ₂₅

  1

  c. log 0,2 = -

  2

  ×××× 25 = ….

  5

  d. log 1 = 0

  ×××× 6 = ….

  ₂

2. Hitung nilai logaritma berikut!

  a. log 256 ₃

  1

  b. log 243

  Jawab: _{2 2 ××××}

  a. log 256 = log 2 ₂ = …. log 2 = …. 1 = …. ₃

  1 ³

  ××××

  b. log = log 3 243 ₃

  = …. log 3 = …. 1 = ….. _{5 3}

  3. log 3x log 125! Tentukan nilai dari

  Jawab: _{5 3 5} log 3x log 125 = log …. ₅ = log ….

  = …. _{2 3} 4. log !

8 Sederhanakan

  Jawab : _{2 3} ×××× ××××

  ××××

  log

  8 = …. log 2 ×××× ××××

  ×××× ×××× ×××× = log ….

  = … x … = ….

  Uji Kompetensi 3

A. Berilah tanda silang (x) huruf a, b, c, d, atau e pada jawaban yang paling benar!\

  _{2 1} 1. log 64 + log 81- log 8 =….

  a. 10 c. 7 e. 4

  b. 9 d. 6 2. Jika log 2 = a, maka log 5 adalah ….

  a. a c. 1 – a e. -1 b.

  1 + 2 d. 3a 3. Jika log 2 = a, maka log 50 adalah ….

  c.

• 1 c. 3a e. 2 - a
₂

  b. 2a d. 2a - 1 3. 4 log 5 = ….

  d.

  0,4 c. 1 e. 25

  b. 0,2 d. 5 4. Jika log (2x + 6), mka x adalah… a.

  46 c. 48 e. 50

  b. 47 d. 49 _{a b c}

  1

  1

  1 æ ö æ ö æ ö 5. log log x log =…..

• b c a

  ç ÷ ç ÷ ç ÷

  è ø è ø è ø

  1 a.

e. 1 - abc -1 c.

  abc

  b. 1 d. 1 + abc _{10 10} 6. log 8 + log 1,25 adalah….

  Bentuk sederhana dari a.

  100 c. 3 e. 1

  b. 10 d. 2 _{3 5} 7. log 5 = p, maka nilai log

3 adalah….

  Jika

  4

  1

  1 a.

  c.

  e.

  p p p

  4

  2

  1 b.

  d.

  p p

  2

  ₃

  1 _{5 2} 8. log . log 8. log 3 adalah….

  Nilai dari

  25 a.

• 3 c. 1 e. 3 b.
• 2 d. 2 _a
₃ 9. = 3, maka log 12 = ….

  Jika 2

  a

  2 a

  1 a.

  2 + +

  c.

  e. 2 +

  2

  1

• a a

  1

• 2 a

  d.

  1 ₃ a a ₅ 10. log 5 = p, maka nilai log 3 adalah….

• b.

  Jika

  1

  1

  4 a.

  c.

  e.

  p p p

  4

  1

  2 b.

  d.

  p p

  2 ₅ 11. log 0,2 = x adalah….

  Nilai x dari

  a. -2 c. 2 e. 4

  b. -1 d. 3 ₂ 12. + 2x – 4 = 0 adalah….

  Himpunan penyelesaian dari log 3x

  5 ü a.

  c. ì- 1, { } 1 e. {-1} í ý

  3 î þ

  5

  5 ì ü ì ü

  b. ,

  1 d.

• í ý í ý

  3

  3 î þ î þ _{2 27 2} 13. log adalah ….

81 Nilai dari

  4

  2

  2 a.

  c.

  e. 1

  3

  3

  4

  3

  2 b.

  d. _{3 3}

  4

  3 14. log 27 sama dengan ….

  a.

  2 c.

  6

  e. 6 b.

  3

  d. 2

  B. Kerjakan soal-soal di bawah ini dengan benar !

  1

  1 1. _{48 16} !

  Tentukan nilai dari log 30 -

• log

  

10 log

  10 Jawab: ....................................................................................................................................

  .................................................................................................................................... .................................................................................................................................... .................................................................................................................................... .................................................................................................................................... .................................................................................................................................... .................................................................................................................................... .................................................................................................................................... .................................................................................................................................... ....................................................................................................................................

  2. Tentukan nilai dari persamaan berikut! a. log 2 + log 18 – log 6 + log 5 – log 3 _{5 5 5}

  b. log 150 - log 24 + log 4 _{3 3 3}

  c. log 81 + log 243 - log 27 Jawab: ....................................................................................................................................

  .................................................................................................................................... .................................................................................................................................... .................................................................................................................................... .................................................................................................................................... .................................................................................................................................... .................................................................................................................................... .................................................................................................................................... .................................................................................................................................... .................................................................................................................................... .................................................................................................................................... .................................................................................................................................... .................................................................................................................................... .................................................................................................................................... .................................................................................................................................... .................................................................................................................................... .................................................................................................................................... .................................................................................................................................... .................................................................................................................................... ....................................................................................................................................

  3. Hitunglah! ₄

  a. log 256 _{3 2 b b b} a b. Jika log a = 6 dan log c = 4, tentukan log _{4 3}

  c

  Jawab: .................................................................................................................................... .................................................................................................................................... .................................................................................................................................... .................................................................................................................................... .................................................................................................................................... .................................................................................................................................... .................................................................................................................................... .................................................................................................................................... .................................................................................................................................... ....................................................................................................................................

  4. Sederhanakan ! _{2 5 4 3 3} a.

  b. log 32 log

  

32

Jawab : ....................................................................................................................................

  .................................................................................................................................... .................................................................................................................................... .................................................................................................................................... .................................................................................................................................... .................................................................................................................................... .................................................................................................................................... .................................................................................................................................... .................................................................................................................................... .................................................................................................................................... _{2 2 2}

  5. log 3 = p dan log 5 = q, nyatakan log 225 dengan p dan q! Misal

  Jawab: .................................................................................................................................... .................................................................................................................................... .................................................................................................................................... .................................................................................................................................... .................................................................................................................................... .................................................................................................................................... .................................................................................................................................... .................................................................................................................................... .................................................................................................................................... .................................................................................................................................... .................................................................................................................................... .................................................................................................................................... .................................................................................................................................... .................................................................................................................................... .................................................................................................................................... .................................................................................................................................... .................................................................................................................................... .................................................................................................................................... .................................................................................................................................... ....................................................................................................................................