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)
[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 logaritma Alokasi Waktu: 26 jam pelajaran (13 x pertemuan) Indikator Pencapaian Hasil Belajar 1. Siswa dapat mengubah bentuk pangkat negatif ke pangkat positf, dan sebaliknya. 2. Siswa dapat mengubah bentuk akar ke bentuk pangkat,dan sebaliknya. 3. Siswa dapat mengubah bentuk pangkat ke bentuk logaritma, dan sebaliknya. 4. Siswa dapat melakukan operasi aljabar pada bentuk pangkat, akar, dan logaritma. 5. Siswa dapat menyederhanakan bentuk aljabar yang memuat pangkat rasional dan logaritma. 6. Siswa dapat merasionalkan bentuk akar. Pertemuan ke-10 s.d. 13 Rangkuman Materi C. Logaritma 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 Sifat-sifat logaritma 1. a
a
log b
=b
2.
a
log (b x c)= a log b + a log c
3.
a
log ç ÷ = a log b - a log c
4.
a
log b n = n a log b
5.
a
6.
a
æbö ècø
c
7.
log b =
c
log b log a
log b x b log c = a log c
an
log b m =
8.
a
log 1 = 0
9.
a
log a n = n
m a . log b n
Matematika X – Semester 1 SMAN 1 Bone-Bone
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Catatan : Logaritma dengan bilangan pokok 10, yakni
10
log x, sering ditulis log x.
Contoh: 1. Sederhanakan 2 log Jawab: 2
1 2 1 + log + 2 log 24 ! 4 3
1 1 1 1 log + 2 log + 2 log 24 =2 log( x x24) 4 3 4 3 2 = log 2 =1
2. Sederhanakan! 2
a. 2 log 3 b. 2 log 98 c. log 150 + log 2 – log 3 Jawab: 2
a. 2 log 3 =3 b. 2 log 98 = 2 log (49. 2) = 2 log ( 7. 7. 2) = 2 log 7 + 2 log 7 + 2 log 2 = 2 2 log 7 + 1
æ 150.2 ö ÷ è 3 ø
c. Log 150 + log 2 – log 3 = log ç
= log 100 =2 3.
Jika 5 log 3 = p tentukan 5 log 75! Jawab: 5 log 75 = 5 log(3 x 5) = 5 log 3 + 5 log 25 = p + 5 log 5 2 = p+2
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Latihan Kerjakan soal-soal di bawah ini dengan benar ! 1. Nyatakan menjadi bentuk pangkat !
1 1 2=2 2 1 b. 3 log = -4 81 1 c. 25 log 0,2 = 2 a. 2 log
5
d. log 1 = 0 Jawab: a. 2 log
b. 3 log
1 2
2 =-
2 ×××× = ….
1 = -4 81
3 ×××× c.
25
1 2
=…..
log 0,2 = -
1 2
25 ×××× = …. 5
d. log 1 = 0 6 ×××× = …. 2. Hitung nilai logaritma berikut! a. 2 log 256 b. 3 log
1 243
Jawab: a. 2 log 256 = 2 log 2 ×××× = …. 2 log 2 = …. 1 = …. b. 3 log
1 243
= 3 log 3 ××××
= …. 3 log 3 = …. 1 = ….. 3. Tentukan nilai dari 5 log 3x 3 log 125! Jawab: 5 log 3x 3 log 125 = 5 log …. = 5 log …. = …. 4. Sederhanakan Jawab : 23
23
log
8! ××××
log
8 = ….
××××
log 2 ××××
×××× ×××× ×××× ××××
×××× = log …. =…x… = ….
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Uji Kompetensi 3 A. Berilah tanda silang (x) huruf a, b, c, d, atau e pada jawaban yang paling benar!\
1
1. 4 log 64 + 3 log 81- 2 log 8 =…. a. 10
c. 7
b. 9
d. 6
e. 4
2. Jika log 2 = a, maka log 5 adalah …. a. a
c. 1 – a
b. 1 + 2
d. 3a
e. -1
3. Jika log 2 = a, maka log 50 adalah …. c. -1
c. 3a
e. 2 - a
b. 2a
d. 2a - 1
3. 4 2 log 5 = …. d. 0,4
c. 1
b. 0,2
d. 5
e. 25
4. Jika log (2x + 6), mka x adalah…
5.
a
a. 46
c. 48
b. 47
d. 49
æ1ö èbø
æ1ö ècø
e. 50
æ1ö èaø
log ç ÷ + b log ç ÷ x c log ç ÷ =…..
1 abc
a. -1
c.
b. 1
d. 1 + abc
6. Bentuk sederhana dari a. 100 b. 10
10
log 8 +
4 p 2 b. p
10
log 1,25 adalah….
c. 3 d. 2
7. Jika 3 log 5 = p, maka nilai 5 log a.
e. 1 - abc
e. 1
3 adalah….
1 p 1 d. 2p
c.
Matematika X – Semester 1 SMAN 1 Bone-Bone
e.
1 4p
22
8. Nilai dari 3 log
1 5 . log 8. 2 log 25
a. -3 b. -2
3 adalah….
c. 1 d. 2
e. 3
9. Jika 2 a = 3, maka 3 log 12 = …. a.
2+a 2
c.
2+a 1+a
b.
2+a a
d. 1 +
e. 2 +
1 a
1 a
10. Jika 3 log 5 = p, maka nilai 5 log 3 adalah….
1 4p 1 b. 2p
1 p 2 d. p
a.
c.
e.
4 p
11. Nilai x dari 5 log 0,2 = x adalah…. a. -2 b. -1
c. 2 d. 3
e. 4
12. Himpunan penyelesaian dari log 3x 2 + 2x – 4 = 0 adalah….
ì 5 ü î 3 þ
c. {1}
a. í- ,1ý
ì 5 î 3
ì5ü î3þ
ü þ
b. í- ,-1ý 13. Nilai dari
14.
2
27
log
d. í ý 2
81 adalah ….
a.
4 3
c.
2 4
b.
3 4
d.
2 3
3 3
e. {-1}
e. 1
2 3
log 27 sama dengan ….
2 b. 3 a.
c.
6
e. 6
d. 2
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B. Kerjakan soal-soal di bawah ini dengan benar ! 1. Tentukan nilai dari log 30 -
48
1 + log 10
16
1 ! log 10
Jawab: .................................................................................................................................... .................................................................................................................................... .................................................................................................................................... .................................................................................................................................... .................................................................................................................................... .................................................................................................................................... .................................................................................................................................... .................................................................................................................................... .................................................................................................................................... .................................................................................................................................... 2. Tentukan nilai dari persamaan berikut! a. log 2 + log 18 – log 6 + log 5 – log 3 b. 5 log 150 - 5 log 24 + 5 log 4 c. 3 log 81 + 3 log 243 - 3 log 27 Jawab: .................................................................................................................................... .................................................................................................................................... .................................................................................................................................... .................................................................................................................................... .................................................................................................................................... .................................................................................................................................... .................................................................................................................................... .................................................................................................................................... .................................................................................................................................... .................................................................................................................................... .................................................................................................................................... .................................................................................................................................... .................................................................................................................................... .................................................................................................................................... .................................................................................................................................... .................................................................................................................................... .................................................................................................................................... .................................................................................................................................... .................................................................................................................................... .................................................................................................................................... 3. Hitunglah! a. 4 log
256 b
b
b
b. Jika log a = 6 dan log c = 4, tentukan log
3
a2
4
c3
Jawab: .................................................................................................................................... .................................................................................................................................... .................................................................................................................................... .................................................................................................................................... .................................................................................................................................... .................................................................................................................................... .................................................................................................................................... .................................................................................................................................... .................................................................................................................................... .................................................................................................................................... Matematika X – Semester 1 SMAN 1 Bone-Bone
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4. Sederhanakan ! a. 2 log 5 32
b.
43
log 3 32
Jawab : .................................................................................................................................... .................................................................................................................................... .................................................................................................................................... .................................................................................................................................... .................................................................................................................................... .................................................................................................................................... .................................................................................................................................... .................................................................................................................................... .................................................................................................................................... .................................................................................................................................... 5. Misal 2 log 3 = p dan 2 log 5 = q, nyatakan 2 log 225 dengan p dan q! Jawab: .................................................................................................................................... .................................................................................................................................... .................................................................................................................................... .................................................................................................................................... .................................................................................................................................... .................................................................................................................................... .................................................................................................................................... .................................................................................................................................... .................................................................................................................................... .................................................................................................................................... .................................................................................................................................... .................................................................................................................................... .................................................................................................................................... .................................................................................................................................... .................................................................................................................................... .................................................................................................................................... .................................................................................................................................... .................................................................................................................................... .................................................................................................................................... ....................................................................................................................................
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