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 |