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A mathematical representation of a logarithm is as follows: logba = c
This means that bc = a
This means that bc = a
Change of Base Formula Calculator
What is Logarithm ?
A logarithm, often referred to as a "log," is a mathematical function that helps you determine how many times you need to multiply a specific number (the base) by itself to obtain another number. In other words, it's the inverse operation of exponentiation. Logarithms are frequently used in mathematics, science, engineering, and other fields.
The basic form of a logarithm is expressed as:
logb(a) = c
- b is the base of the logarithm.
- a is the number for which you want to find the logarithm.
- c is the result, indicating how many times you must raise the base b to get a.
Example:
If the base is 10 (this is the most common base and is called the common logarithm), the logarithm of the number 100 with base 10 is 2 because 102 = 100. So, we have log 10100 = 2.
Logarithm rules
Product rule
logb(a × c) = logb(a)+logb(c)
Quotient rule
logb(
ac
) = logb(a)-logb(c)Power rule
logb(ac) = c × logb(a)
Base switch rule
logb(c) =
1logc(b)
Change of base rule
logb(a) =
logc(a)logc(b)
See also
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