A logarithm is the power to which a number must be raised to get another number. Example: Since 102 = 100, logarithm 100 = 2. This is one of the examples of the base ten logarithm. The name is due to the fact that ten is the number that is exponentiated. A wide range of base units is used for logarithmic calculations. For example, 3 is the base for eight, since two raised to the power of three makes eight.
Since 23 = 8, logarithm2 8 = 3. The logarithm must always be written so that the base number is subscript. Logarithms with a base of 10 and natural logarithms are the most common types of logarithm. They always have special notations.
What are the properties of the logarithm?
Logarithms have a number of useful properties, which is why scientists have been quick to adopt them. First, they are the best solutions for avoiding long, tedious calculations. For example, scientists can use a special table to look up the logarithm of any number. They then add the logarithms together before consulting the table again to identify the number with the calculated logarithm.
History of the logarithm
The invention of logarithms was the result of comparing geometric and arithmetic sequences. Each time a constant arises in a geometric sequence, and each constant has a successor. Example: ... 1/1,000, 1/100, 1/10, 1, 10, 100, 1,000... has ten as a constant quotient. In arithmetic sequence, all successive terms differ by a constant. They are also called common difference. Example: ... 3, 2, 1, 0, 1, 2, 3... has 1 as the common difference.
Note that it is possible to write a geometric sequence in terms of its constant quotient. Take a look at the example below:
... 10 x 3, 10, 2, 10, 100, 101, 102, 103.
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The logarithm is a tool used by scientists and mathematicians to perform complex calculations. It was invented in the 17th century and has since been adopted in a variety of fields that rely heavily on calculations.