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Calculators: Logarithm | Ratio | Doubling | Tenfold | Multifold
Calculate Logarithm
The logarithm for an user-defined base can be calculated as well as all inverse calculations. The logarithm is the inverse operation to the exponentiation (power function).
Formulas: logb(a)=x, a=bx
Insert two values, the third value will be calculated. Input values can be numbers e as Euler's number. The maximal value for the decimal places is 15.
The logarithm of a number is the exponent by which a base must be multiplied to obtain a certain result. The base gives the logarithm its name, for example ten for the base 10 logarithm. This one is very common and is often used when the values cover a very large range from very small to very large. If values in the base 10 logarithm are increased by one, the actual value increases tenfold. It is used prominently in the Richter scale for earthquakes, where an earthquake of magnitude six is ten times as strong as one of magnitude five and one hundred times as strong as one of magnitude four. The base 10 logarithm is often written as lg. See also Calculating with different logarithmic scales.
Euler's number e is a very special one; the logarithm of this base is called the natural logarithm and is often written as ln. The number e plays a central role in many areas of mathematics. The inverse of the natural logarithm is the exponential function ex, which is equal to its own derivative.
The logarithm to base two is called the dual logarithm and is written as ld. It plays a central role in computer science, where powers of two are often used. Each step doubles the value.
Although logarithms were already known in ancient times, they were not used extensively until the 17th century. The breakthrough was the publication of the first logarithm tables by John Napier in 1614. Logarithms saved a huge amount of time in many calculations at the time.
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German: Logarithmus berechnen
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