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Logarithm Calculator
Log calculator finds the logarithm function result (can be called exponent) from the given base number and a real number. LogarithmLogarithm is considered to be one of the basic concepts in mathematics. There are plenty of definitions, starting from really complicated and ending up with rather simple ones. In order to answer a question, what a logarithm is, let's take a look at the table below: log base 1 log base 2 log base 3 log base 4 log base 5 log base 6 212223242526 248163264This is the table in which we can see the values of two squared, two cubed, and so on. This is an operation in mathematics, known as exponentiation. If we look at the numbers at the bottom line, we can try to find the power value to which 2 must be raised to get this number. For example, to get 16, it is necessary to raise two to the fourth power. And to get a 64, you need to raise two to the sixth power. Therefore, logarithm is the exponent to which it is necessary to raise a fixed number (which is called the base), to get the number y. In other words, a logarithm can be represented as the following: logb x = y with b being the base, x being a real number, and y being an exponent. For example, 23 = 8 ⇒ log2 8 = 3 (the logarithm of 8 to base 2 is equal to 3, because 23 = 8). Similarly, log2 64 = 6, because 26 = 64. Therefore, it is obvious that logarithm operation is an inverse one to exponentiation. log base 1 log base 2 log base 3 log base 4 log base 5 log base 6 212223242526 248163264 log22 = 1 log24 = 2 log28 = 3 log216 = 4 log232 = 5 log264 = 6Unfortunately, not all logarithms can be calculated that easily. For example, finding log2 5 is hardly possible by just using our simple calculation abilities. After using logarithm calculator, we can find out that log2 5 = 2,32192809 There are a few specific types of logarithms. For example, the logarithm to base 2 is known as the binary logarithm, and it is widely used in computer science and programming languages. The logarithm to base 10 is usually referred to as the common logarithm, and it has a huge number of applications in engineering, scientific research, technology, etc. Finally, so called natural logarithm uses the number e (which is approximately equal to 2.71828) as its base, and this kind of logarithm has a great importance in mathematics, physics, and other precise sciences. The logarithm logb(x) = y is read as log base b of x is equals to y. Please note that the base of log number b must be greater than 0 and must not be equal to 1. And the number (x) which we are calculating log base of (b) must be a positive real number. For example log 2 of 8 is equal to 3. log2(8) = 3 (log base 2 of 8) The exponential is 23 = 8 Common Values for Log Base Log BaseLog NameNotationLog Example 2binary logarithmlb(x)log2(16) = lb(16) = 4 => 24 = 16 10common logarithmlg(x)log10(1000) = lg(1000) = 3 => 103 = 1000 enatural logarithmln(x)loge(8) = ln(8) = 2.0794 => e2.0794 = 8 Logarithmic IdentitiesList of logarithmic identites, formulas and log examples in logarithm form. Logarithm of a Product logb(x·y) = logb(x) + logb(y) log2(5·7) = log2(5) + log2(7) Logarithm of a Quotient logb(x/y) = logb(x) - logb(y) log2(5/7) = log2(5) - log2(7) Logarithm of a Power logb(xy) = y·logb(x) log2(57) = 7·log2(5) Change of Base logb(x) = (logk(x)) / (logk(b)) Natural Logarithm Examples ln(2) = loge(2) = 0.6931 ln(3) = loge(3) = 1.0986 ln(4) = loge(4) = 1.3862 ln(5) = loge(5) = 1.609 ln(6) = loge(6) = 1.7917 ln(10) = loge(10) = 2.3025 Logarithm Values TablesList of log function values tables in common base numbers. log2(x)NotationValue log2(1)lb(1)0 log2(2)lb(2)1 log2(3)lb(3)1.584963 log2(4)lb(4)2 log2(5)lb(5)2.321928 log2(6)lb(6)2.584963 log2(7)lb(7)2.807355 log2(8)lb(8)3 log2(9)lb(9)3.169925 log2(10)lb(10)3.321928 log2(11)lb(11)3.459432 log2(12)lb(12)3.584963 log2(13)lb(13)3.70044 log2(14)lb(14)3.807355 log2(15)lb(15)3.906891 log2(16)lb(16)4 log2(17)lb(17)4.087463 log2(18)lb(18)4.169925 log2(19)lb(19)4.247928 log2(20)lb(20)4.321928 log2(21)lb(21)4.392317 log2(22)lb(22)4.459432 log2(23)lb(23)4.523562 log2(24)lb(24)4.584963 log10(x)NotationValue log10(1)log(1)0 log10(2)log(2)0.30103 log10(3)log(3)0.477121 log10(4)log(4)0.60206 log10(5)log(5)0.69897 log10(6)log(6)0.778151 log10(7)log(7)0.845098 log10(8)log(8)0.90309 log10(9)log(9)0.954243 log10(10)log(10)1 log10(11)log(11)1.041393 log10(12)log(12)1.079181 log10(13)log(13)1.113943 log10(14)log(14)1.146128 log10(15)log(15)1.176091 log10(16)log(16)1.20412 log10(17)log(17)1.230449 log10(18)log(18)1.255273 log10(19)log(19)1.278754 log10(20)log(20)1.30103 log10(21)log(21)1.322219 log10(22)log(22)1.342423 log10(23)log(23)1.361728 log10(24)log(24)1.380211 loge(x)NotationValue loge(1)ln(1)0 loge(2)ln(2)0.693147 loge(3)ln(3)1.098612 loge(4)ln(4)1.386294 loge(5)ln(5)1.609438 loge(6)ln(6)1.791759 loge(7)ln(7)1.94591 loge(8)ln(8)2.079442 loge(9)ln(9)2.197225 loge(10)ln(10)2.302585 loge(11)ln(11)2.397895 loge(12)ln(12)2.484907 loge(13)ln(13)2.564949 loge(14)ln(14)2.639057 loge(15)ln(15)2.70805 loge(16)ln(16)2.772589 loge(17)ln(17)2.833213 loge(18)ln(18)2.890372 loge(19)ln(19)2.944439 loge(20)ln(20)2.995732 loge(21)ln(21)3.044522 loge(22)ln(22)3.091042 loge(23)ln(23)3.135494 loge(24)ln(24)3.178054 Facebook Twitter Related Log Base Calculators Natural Logarithm ln(x) Calculator Common Log base 10 Calculator Log base 2 Calculator© 2019-2024 www.LogCalculator.net Privacy Policy and Cookies Contact Us Sitemap |
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