The logarithm of a number to a given base is the exponent to which the base must be raised to produce the number. In mathematical terms, if 'b' is the base and 'x' is the number, then the logarithm of 'x' to the base 'b' is written as logb(x) and is defined as the exponent 'y' such that b^y = x.
The logarithm of a number to a given base is a useful tool in many areas of mathematics and science, including finance, engineering, and physics. It's also used in solving exponential equations and in graphing logarithmic functions.
In mathematics, the most common logarithms are logarithms to the base 10, which are called common logarithms, and logarithms to the base e, which are called natural logarithms. The natural logarithm is denoted by the symbol ln, and has special properties in calculus and other areas of mathematics.
To calculate any "log base of" use this fromula, which is given below-
Where,
| logb(x) | Equal to |
|---|---|
| log2(4) | 2 |
| log2(8) | 3 |
| log8(3) | 0.52832083357372 |
| log2(2) | 1 |
| log2(1000) | 9.9657842846621 |
| log2(3) | 1.5849625007212 |
| log2(1) | 0 |
| log2(6) | 2.5849625007212 |
| log4(2) | 0.5 |
| log2(10) | 3.3219280948874 |
| log2(0) | -INF |
| log2(256) | 8 |
| log2(9) | 3.1699250014423 |
| log3(7) | 1.7712437491614 |
| log10(10) | 1 |
| log4(16) | 2 |
| log5(1) | 0 |
| log10(1) | 0 |
| log2(1024) | 10 |
| log3(1) | 0 |
| log5(2) | 0.43067655807339 |
| log8(2) | 0.33333333333333 |
| log2(5) | 2.3219280948874 |
| log2(1000000) | 19.931568569324 |
| log3(9) | 2 |
| log3(27) | 3 |
| log2(32) | 5 |
| log10(0) | -INF |
| log1(2) | NAN |
| log4(5) | 1.1609640474437 |
| log2(16) | 4 |
| log2(2048) | 11 |
| log3(2) | 0.63092975357146 |
| log6(36) | 2 |
| log2(512) | 9 |
| log2(11) | 3.4594316186373 |
| log10(5) | 0.69897000433602 |
| log1(1) | NAN |
| log10(100) | 2 |
| log2(12) | 3.5849625007212 |
| log4(1) | 0 |
| log2(15) | 3.9068905956085 |
| log2(10000) | 13.287712379549 |
| log3(5) | 1.4649735207179 |
| log10(1000) | 3 |
| log5(125) | 3 |
| log3(6) | 1.6309297535715 |
| log2(65536) | 16 |
| log3(3) | 1 |
| log27(9) | 0.66666666666667 |
| log2(7) | 2.8073549220576 |
| log5(3) | 0.68260619448599 |
| log8(4) | 0.66666666666667 |
| log3(4) | 1.2618595071429 |
| log4(4) | 1 |
| log3(8) | 1.8927892607144 |
| log3(10) | 2.0959032742894 |
| log5(625) | 4 |
| log2(4096) | 12 |
| log2(20) | 4.3219280948874 |
| log9(3) | 0.5 |
| log8(8) | 1 |
| log10(3) | 0.47712125471966 |
| log4(3) | 0.79248125036058 |
| log2(128) | 7 |
| log2(500) | 8.9657842846621 |
| log5(25) | 2 |
| log16(4) | 0.5 |
| log3(243) | 5 |
| log2(4000) | 11.965784284662 |
| log2(100000) | 16.609640474437 |
| log6(216) | 3 |
| log2(8192) | 13 |
| log25(5) | 0.5 |
| log5(7) | 1.2090619551222 |
| log2(100) | 6.6438561897747 |
| log4(8) | 1.5 |
| log7(49) | 2 |
| log2(50) | 5.6438561897747 |
| log7(1) | 0 |
| log2(200) | 7.6438561897747 |
| log2(40) | 5.3219280948874 |
| log2(64) | 6 |
| log16(2) | 0.25 |
| log4(7) | 1.4036774610288 |
| log16(8) | 0.75 |
| log8(20) | 1.4406426982958 |
| log3(81) | 4 |
| log4(64) | 3 |
| log4(6) | 1.2924812503606 |
| log5(10) | 1.4306765580734 |
| log5(6) | 1.1132827525594 |
| log5(8) | 1.2920296742202 |
| log10(2) | 0.30102999566398 |
| log7(9) | 1.1291500681072 |
| log3(12) | 2.2618595071429 |
| log10(4) | 0.60205999132796 |
| log5(5) | 1 |
| log2(30) | 4.9068905956085 |
| log5(50) | 2.4306765580734 |
| log3(20) | 2.7268330278608 |
| log4(20) | 2.1609640474437 |
| log4(32) | 2.5 |
| log2(25) | 4.6438561897747 |
| log10(7) | 0.84509804001426 |
| log2(255) | 7.9943534368589 |
| log3(0) | -INF |
| log2(16384) | 14 |
| log9(81) | 2 |
| log2(32768) | 15 |
| log81(3) | 0.25 |
| log2(13) | 3.7004397181411 |
| log8(64) | 2 |
| log10(1000000) | 6 |
| log8(1) | 0 |
| log2(24) | 4.5849625007212 |
| log3(18) | 2.6309297535715 |
| log8(32) | 1.6666666666667 |
| log2(5000) | 12.287712379549 |
| log64(2) | 0.16666666666667 |
| log36(6) | 0.5 |
| log5(100) | 2.8613531161468 |
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