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# LOGARITMA - PowerPoint PPT Presentation

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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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

• 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

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

1. Jika 2log x = 3

Tentukan nilai x = ….

Jawab:

2log x = 3  x = 23

x = 8.

2. Jika 4log 64 = x

Tentukan nilai x = ….

Jawab:

4log 64 = x  4x = 64

4x = 44

x = 4.

3. Nilai dari 2log 8 + 3log 9 = ….

Jawab:

= 2log 8 + 3log 9

= 2log 23 + 3log 32

= 3 + 2

= 5

4. Nilai dari 2log (8 x 16) = ….

Jawab:

= 2log 8 + 2log 16

= 2log 23 + 2log 24

= 3 + 4

= 7

5. Nilai dari 3log (81 : 27) = ….

Jawab:

= 3log 81 - 3log 27

= 3log 34 - 3log 33

= 4 - 3

= 1

6. Nilai dari 2log 84 = ….

Jawab:

= 2log 84

= 4 x 2log 23

= 4 x 3

= 12

2log 8

=

4

2

Contoh Soal

7. Nilai dari 2log 84 = ….

Jawab:

= 2log 84

= 2 x 2log 23

= 2 x 3

= 6

8. Jika log 100 = x

Tentukan nilai x = ….

Jawab:

log 100 = x  10x = 100

10x = 102

x = 2.

log 3 = 0,477 dan log 2 = 0,301

Nilai log 18 = ….

a. 1,552

b. 1,525

c. 1,255

d. 1,235

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

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

log 2 = 0,301 dan log 5 = 0,699

Nilai log 5 + log 8 + log 25 = ….

a. 2

b. 3

c. 4

d. 5

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

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

Diketahui log 4,72 = 0,674

Nilai dari log 4.720 = ….

a. 1,674

b. 2,674

c. 3,674

d. 4,674

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

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

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

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

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

Diketahui log 3 = a dan log 2 = b. Maka log 18 = ….

a. 2a – b

b. 2a + b

c. a + 2b

d. a – 2b

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

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

Diketahui plog 27 = 3x

Maka plog 243 = ….

a. 4x

b. 5x

c. 6x

d. 7x

plog 27 = 3x

33 = p3x

Maka: x = 1 dan p = 3

plog 243 = 3log (3)5

= 5.3log 3

= 5 . X

= 5x

Diketahui plog 27 = 3x

Maka plog 243 = ….

a. 4x

b. 5x

c. 6x

d. 7x

b. 5x

Diketahui log 2 = 0,301

Maka log 50 = ….

a. 0,699

b. 1,301

c. 1,699

d. 2,301

log 2 = 0,301

log 50 = log (100 : 2)

= log 100 – log 2

= log 102 – log 2

= 2 – 0,301

= 1,699

Diketahui log 2 = 0,301

Maka log 50 = ….

a. 0,699

b. 1,301

c. 1,699

d. 2,301

c. 1,699

Jangan Lewatkan

Program Khusus

Pembahasan Soal-soal

UN 2001 s.d. 2005