Logaritma adalah konsep matematika yang berkaitan dengan pengukuran kekuatan atau eksponen dari suatu bilangan. Secara sederhana, logaritma adalah operasi invers dari eksponensiasi.
Jika kita memiliki persamaan:
Maka logaritma dari dengan basis adalah:
Ini berarti bahwa logaritma terhadap basis adalah nilai yang harus dipangkatkan pada agar hasilnya menjadi .
Contoh sederhana:
- maka
- maka
Logaritma memiliki banyak aplikasi dalam ilmu pengetahuan, termasuk dalam statistik, ilmu komputer, dan ekonomi. Beberapa jenis logaritma yang sering digunakan adalah:
- Logaritma Basis 10 (Logaritma Desimal): Ditulis sebagai .
- Logaritma Basis (Logaritma Natural): Ditulis sebagai , di mana adalah bilangan Euler (sekitar 2.71828).
- Logaritma Basis 2: Umum digunakan dalam ilmu komputer, ditulis sebagai .
Logaritma juga memiliki sifat-sifat tertentu, seperti:
- (sifat hasil kali)
- (sifat hasil bagi)
- (sifat pangkat)
Sifat-sifat ini membuat logaritma sangat berguna dalam menyederhanakan perhitungan, terutama dalam konteks eksponensial.
Contoh Tabel Logaritma
| x | log₁₀(x) | log₂(x) |
|---|---|---|
| 1 | 0 | 0 |
| 2 | 0.301 | 1 |
| 3 | 0.477 | 1.585 |
| 4 | 0.602 | 2 |
| 5 | 0.699 | 2.322 |
| 6 | 0.778 | 2.585 |
| 7 | 0.845 | 2.807 |
| 8 | 0.903 | 3 |
| 9 | 0.954 | 3.170 |
| 10 | 1 | 3.321 |
| 100 | 2 | 6.644 |
| 1000 | 3 | 9.965 |
Hitung Manual
Tabel Logaritma (basis 10) untuk 1 hingga 100
| x | log₁₀(x) |
|---|---|
| 1 | log_{10}(1) = 0.0000 |
| 2 | log_{10}(2) = 0.3010 |
| 3 | log_{10}(3) = 0.4771 |
| 4 | log_{10}(4) = 0.6021 |
| 5 | log_{10}(5) = 0.6990 |
| 6 | log_{10}(6) = 0.7782 |
| 7 | log_{10}(7) = 0.8451 |
| 8 | log_{10}(8) = 0.9031 |
| 9 | log_{10}(9) = 0.9542 |
| 10 | log_{10}(10) = 1.0000 |
| 11 | log_{10}(11) = 1.0414 |
| 12 | log_{10}(12) = 1.0792 |
| 13 | log_{10}(13) = 1.1139 |
| 14 | log_{10}(14) = 1.1461 |
| 15 | log_{10}(15) = 1.1761 |
| 16 | log_{10}(16) = 1.2041 |
| 17 | log_{10}(17) = 1.2304 |
| 18 | log_{10}(18) = 1.2553 |
| 19 | log_{10}(19) = 1.2788 |
| 20 | log_{10}(20) = 1.3010 |
| 21 | log_{10}(21) = 1.3222 |
| 22 | log_{10}(22) = 1.3424 |
| 23 | log_{10}(23) = 1.3617 |
| 24 | log_{10}(24) = 1.3802 |
| 25 | log_{10}(25) = 1.3979 |
| 26 | log_{10}(26) = 1.4150 |
| 27 | log_{10}(27) = 1.4314 |
| 28 | log_{10}(28) = 1.4472 |
| 29 | log_{10}(29) = 1.4624 |
| 30 | log_{10}(30) = 1.4771 |
| 31 | log_{10}(31) = 1.4914 |
| 32 | log_{10}(32) = 1.5051 |
| 33 | log_{10}(33) = 1.5185 |
| 34 | log_{10}(34) = 1.5315 |
| 35 | log_{10}(35) = 1.5441 |
| 36 | log_{10}(36) = 1.5563 |
| 37 | log_{10}(37) = 1.5682 |
| 38 | log_{10}(38) = 1.5798 |
| 39 | log_{10}(39) = 1.5911 |
| 40 | log_{10}(40) = 1.6021 |
| 41 | log_{10}(41) = 1.6128 |
| 42 | log_{10}(42) = 1.6232 |
| 43 | log_{10}(43) = 1.6335 |
| 44 | log_{10}(44) = 1.6435 |
| 45 | log_{10}(45) = 1.6532 |
| 46 | log_{10}(46) = 1.6628 |
| 47 | log_{10}(47) = 1.6721 |
| 48 | log_{10}(48) = 1.6812 |
| 49 | log_{10}(49) = 1.6902 |
| 50 | log_{10}(50) = 1.6990 |
| 51 | log_{10}(51) = 1.7076 |
| 52 | log_{10}(52) = 1.7160 |
| 53 | log_{10}(53) = 1.7243 |
| 54 | log_{10}(54) = 1.7324 |
| 55 | log_{10}(55) = 1.7404 |
| 56 | log_{10}(56) = 1.7482 |
| 57 | log_{10}(57) = 1.7559 |
| 58 | log_{10}(58) = 1.7634 |
| 59 | log_{10}(59) = 1.7709 |
| 60 | log_{10}(60) = 1.7782 |
| 61 | log_{10}(61) = 1.7853 |
| 62 | log_{10}(62) = 1.7924 |
| 63 | log_{10}(63) = 1.7993 |
| 64 | log_{10}(64) = 1.8062 |
| 65 | log_{10}(65) = 1.8129 |
| 66 | log_{10}(66) = 1.8195 |
| 67 | log_{10}(67) = 1.8261 |
| 68 | log_{10}(68) = 1.8325 |
| 69 | log_{10}(69) = 1.8388 |
| 70 | log_{10}(70) = 1.8451 |
| 71 | log_{10}(71) = 1.8513 |
| 72 | log_{10}(72) = 1.8573 |
| 73 | log_{10}(73) = 1.8633 |
| 74 | log_{10}(74) = 1.8692 |
| 75 | log_{10}(75) = 1.8751 |
| 76 | log_{10}(76) = 1.8808 |
| 77 | log_{10}(77) = 1.8865 |
| 78 | log_{10}(78) = 1.8921 |
| 79 | log_{10}(79) = 1.8976 |
| 80 | log_{10}(80) = 1.9031 |
| 81 | log_{10}(81) = 1.9085 |
| 82 | log_{10}(82) = 1.9138 |
| 83 | log_{10}(83) = 1.9191 |
| 84 | log_{10}(84) = 1.9243 |
| 85 | log_{10}(85) = 1.9294 |
| 86 | log_{10}(86) = 1.9345 |
| 87 | log_{10}(87) = 1.9395 |
| 88 | log_{10}(88) = 1.9445 |
| 89 | log_{10}(89) = 1.9494 |
| 90 | log_{10}(90) = 1.9542 |
| 91 | log_{10}(91) = 1.9590 |
| 92 | log_{10}(92) = 1.9638 |
| 93 | log_{10}(93) = 1.9685 |
| 94 | log_{10}(94) = 1.9731 |
| 95 | log_{10}(95) = 1.9777 |
| 96 | log_{10}(96) = 1.9823 |
| 97 | log_{10}(97) = 1.9868 |
| 98 | log_{10}(98) = 1.9912 |
| 99 | log_{10}(99) = 1.9956 |
| 100 | log_{10}(100) = 2.0000 |
