logaritma
TRANSCRIPT
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Pengertian LogaritmaPengertian Logaritma
PPlog a = m artinya a = plog a = m artinya a = pmm Keterangan:Keterangan:p disebut bilangan pokokp disebut bilangan pokoka disebut bilangan logaritma atau a disebut bilangan logaritma atau
numerus dengan a > 0numerus dengan a > 0m disebut hasil logaritma atau eksponen m disebut hasil logaritma atau eksponen
dari basisdari basis
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Logaritma dengan basis 10Logaritma dengan basis 10
Pada bentuk Pada bentuk pplog a = m, maka: log a = m, maka: 1010log a = m cukup ditulis log a = m.log a = m cukup ditulis log a = m.
Basis 10 pada logaritma tidak perlu Basis 10 pada logaritma tidak perlu dituliskan.dituliskan.
Contoh:Contoh:1010log 3 log 3 dituliskan log 3 dituliskan log 31010log 5 log 5 dituliskan log 5 dituliskan log 5
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Sifat-sifat LogaritmaSifat-sifat Logaritma
1. 1. pplog (a x b) = log (a x b) = pplog a + log a + pplog blog b
2.2. p plog (a : b) = log (a : b) = pplog a - log a - pplog blog b
3.3. pplog (a)log (a)nn = n x = n x pplog alog a
n ma = = pplog (a)log (a) nm
4. 4. pploglog
nm pplog alog a==
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Contoh SoalContoh Soal
1. Jika 1. Jika 22log x = 3log x = 3 Tentukan nilai x = ….Tentukan nilai x = ….
Jawab:Jawab:22log x = 3 log x = 3 x = 2 x = 233
x = 8.x = 8.
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Contoh SoalContoh Soal
2. Jika 2. Jika 44log 64 = xlog 64 = x Tentukan nilai x = ….Tentukan nilai x = ….
Jawab:Jawab:44log 64 = x log 64 = x 4 4xx = 64 = 64
44xx = 4 = 444
x = 4.x = 4.
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Contoh SoalContoh Soal
3. Nilai dari 3. Nilai dari 22log 8 + log 8 + 33log 9 = ….log 9 = ….
Jawab:Jawab:= = 22log 8 + log 8 + 33log 9log 9
= = 22log 2log 233 + + 33log 3log 322
= 3 + 2= 3 + 2= 5= 5
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Contoh SoalContoh Soal
4. Nilai dari 4. Nilai dari 22log (8 x 16) = ….log (8 x 16) = ….
Jawab:Jawab:= = 22log 8 + log 8 + 22log 16log 16
= = 22log 2log 233 + + 22log 2log 244
= 3 + 4= 3 + 4= 7= 7
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Contoh SoalContoh Soal
5. Nilai dari 5. Nilai dari 33log (81 : 27) = ….log (81 : 27) = ….
Jawab:Jawab:= = 33log 81 - log 81 - 33log 27log 27
= = 33log 3log 344 - - 33log 3log 333
= 4 - 3= 4 - 3= 1= 1
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Contoh SoalContoh Soal
6. Nilai dari 6. Nilai dari 22log 8log 844 = …. = ….
Jawab:Jawab:= = 22log 8log 844
= 4 x = 4 x 22log 2log 233
= 4 x 3= 4 x 3= 12= 12
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Contoh SoalContoh Soal
7. Nilai dari 7. Nilai dari 22log log √√8844 = …. = ….
Jawab:Jawab:= = 22log log √√8844
= 2 x = 2 x 22log 2log 233
= 2 x 3= 2 x 3= 6= 6
24 22log 8log 8==
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Contoh SoalContoh Soal
8. Jika log 100 = x8. Jika log 100 = x Tentukan nilai x = ….Tentukan nilai x = ….
Jawab:Jawab:log 100 = x log 100 = x 10 10xx = 100 = 100
1010xx = 10 = 1022
x = 2.x = 2.
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Soal - 1Soal - 1
log 3 = 0,477 dan log 2 = 0,301log 3 = 0,477 dan log 2 = 0,301Nilai log 18 = ….Nilai log 18 = ….a.a. 1,5521,552b.b. 1,5251,525c.c. 1,2551,255d.d. 1,2351,235
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PembahasanPembahasan
log 3 = 0,477 dan log 2 = 0,301log 3 = 0,477 dan log 2 = 0,301log 18 = log 9 x 2log 18 = log 9 x 2
= log 9 + log 2= log 9 + log 2= log 3= log 322 + log 2 + log 2= 2 (0,477) + 0,301= 2 (0,477) + 0,301= 0,954 + 0,301= 0,954 + 0,301= 1,255 = 1,255
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JawabanJawaban
log 3 = 0,477 dan log 2 = 0,301log 3 = 0,477 dan log 2 = 0,301Nilai log 18 = ….Nilai log 18 = ….a.a. 1,5521,552b.b. 1,5251,525c.c. 1,2551,255d.d. 1,2351,235
c. 1,255c. 1,255
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Soal - 2Soal - 2
log 2 = 0,301 dan log 5 = 0,699log 2 = 0,301 dan log 5 = 0,699Nilai log 5 + log 8 + log 25 = ….Nilai log 5 + log 8 + log 25 = ….a.a. 22b.b. 33c.c. 44d.d. 55
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PembahasanPembahasan
log 2 = 0,301 dan log 5 = 0,699log 2 = 0,301 dan log 5 = 0,699= log 5 + log 8 + log 25= log 5 + log 8 + log 25= log 5 + log 2= log 5 + log 233 + log 5 + log 522
= log 5 + 3.log 2 + 2.log 5= log 5 + 3.log 2 + 2.log 5= 0,699 + 3(0,301) + 2(0,699)= 0,699 + 3(0,301) + 2(0,699)= 0,699 + 0,903 + 1,398= 0,699 + 0,903 + 1,398= 3,0= 3,0
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JawabanJawaban
log 2 = 0,301 dan log 5 = 0,699log 2 = 0,301 dan log 5 = 0,699Nilai log 5 + log 8 + log 25 = ….Nilai log 5 + log 8 + log 25 = ….a.a. 22b.b. 33c.c. 44d.d. 55
b. 3b. 3
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Soal - 3Soal - 3
Diketahui log 4,72 = 0,674Diketahui log 4,72 = 0,674Nilai dari log 4.720 = ….Nilai dari log 4.720 = ….a.a. 1,6741,674b.b. 2,6742,674c.c. 3,6743,674d.d. 4,6744,674
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PembahasanPembahasan
log 4,72 = 0,674log 4,72 = 0,674log 4.720 = log (4,72 x 1000)log 4.720 = log (4,72 x 1000) = log 4,72 + log 1000= log 4,72 + log 1000
= log 4,72 + log 10= log 4,72 + log 1033
= 0,674 + 3= 0,674 + 3 = 3,674= 3,674
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JawabanJawaban
Diketahui log 4,72 = 0,674Diketahui log 4,72 = 0,674Nilai dari log 4.720 = ….Nilai dari log 4.720 = ….a.a. 1,6741,674b.b. 2,6742,674c.c. 3,6743,674d.d. 4,6744,674
c. 3,674c. 3,674
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Soal - 4Soal - 4
Diketahui log 3 = 0,477 dan Diketahui log 3 = 0,477 dan log 5 = 0,699. Nilai log 135 = ….log 5 = 0,699. Nilai log 135 = ….a.a. 2,7782,778b.b. 2,7322,732c.c. 2,1762,176d.d. 2,1302,130
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PembahasanPembahasan
log 3 = 0,477 dan log 5 = 0,699. log 3 = 0,477 dan log 5 = 0,699. log 135 = log (27 x 5)log 135 = log (27 x 5)
= log 27 + log 5= log 27 + log 5= log 3= log 333 + log 5 + log 5= 3(0,477) + 0,699= 3(0,477) + 0,699= 1,431 + 0,699= 1,431 + 0,699= 2,130= 2,130
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JawabanJawaban
Diketahui log 3 = 0,477 dan Diketahui log 3 = 0,477 dan log 5 = 0,699. Nilai log 135 = ….log 5 = 0,699. Nilai log 135 = ….a.a. 2,7782,778b.b. 2,7322,732c.c. 2,1762,176d.d. 2,1302,130
d. 2,130d. 2,130
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Soal - 5Soal - 5
Diketahui log 3 = a dan log 2 = b. Diketahui log 3 = a dan log 2 = b. Maka log 18 = ….Maka log 18 = ….a.a. 2a – b2a – bb.b. 2a + b2a + bc.c. a + 2ba + 2bd.d. a – 2ba – 2b
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PembahasanPembahasan
Diketahui log 3 = a dan log 2 = b. Diketahui log 3 = a dan log 2 = b. log 18 = log (9 x 2)log 18 = log (9 x 2)
= log 9 + log 2= log 9 + log 2= log 3= log 322 + log 2 + log 2= 2.log 3 + log b= 2.log 3 + log b= 2(a) + b= 2(a) + b= 2a + b= 2a + b
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JawabanJawaban
Diketahui log 3 = a dan log 2 = b. Diketahui log 3 = a dan log 2 = b. Maka log 18 = ….Maka log 18 = ….a.a. 2a – b2a – bb.b. 2a + b2a + bc.c. a + 2ba + 2bd.d. a – 2ba – 2b
b. 2a + bb. 2a + b
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Soal - 6Soal - 6
Diketahui Diketahui pplog 27 = 3x log 27 = 3x Maka Maka pplog 243 = ….log 243 = ….a.a. 4x4xb.b. 5x5xc.c. 6x6xd.d. 7x7x
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PembahasanPembahasan
pplog 27 = 3x log 27 = 3x 3333 = p = p3x3x Maka: x = 1 dan p = 3 Maka: x = 1 dan p = 3 pplog 243 = log 243 = 33log (3)log (3)55
= 5.= 5.33log 3log 3= 5 . X= 5 . X= 5x= 5x
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JawabanJawaban
Diketahui Diketahui pplog 27 = 3x log 27 = 3x Maka Maka pplog 243 = ….log 243 = ….a.a. 4x4xb.b. 5x5xc.c. 6x6xd.d. 7x7x
b. 5xb. 5x
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Soal - 7Soal - 7
Diketahui log 2 = 0,301 Diketahui log 2 = 0,301 Maka log 50 = ….Maka log 50 = ….a.a. 0,6990,699b.b. 1,3011,301c.c. 1,6991,699d.d. 2,3012,301
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PembahasanPembahasan
log 2 = 0,301 log 2 = 0,301 log 50 log 50 = log (100 : 2)= log (100 : 2)
= log 100 – log 2= log 100 – log 2= log 10= log 1022 – log 2 – log 2 = 2 – 0,301= 2 – 0,301= 1,699= 1,699
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JawabanJawaban
Diketahui log 2 = 0,301 Diketahui log 2 = 0,301 Maka log 50 = ….Maka log 50 = ….a.a. 0,6990,699b.b. 1,3011,301c.c. 1,6991,699d.d. 2,3012,301
c. 1,699c. 1,699
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Jangan LewatkanJangan Lewatkan
Program KhususProgram Khusus
Pembahasan Soal-soalPembahasan Soal-soal
UN 2001 s.d. 2005UN 2001 s.d. 2005