# Logarithm Calculator

A mathematical representation of a logarithm is as follows: log

This means that

*=*_{b}a*c*This means that

*b*^{c}= 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:

log* _{b}(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 **10 ^{2} = 100**. So, we have

**log**.

_{10}100 = 2### Logarithm rules

#### Product rule

log* _{b}*(

*a*×

*c*) = log

*(*

_{b}*a*)

*+*log

*(*

_{b}*c*)

#### Quotient rule

log) = log

*(*_{b}*a*

*c*

*(*_{b}*a*)*-*log*(*_{b}*c*)#### Power rule

log* _{b}*(

*a*) =

^{c}*c*× log

*(*

_{b}*a*)

#### Base switch rule

log

*(*_{b}*c*) =1log

*(*_{c}*b*)#### Change of base rule

log

*(*_{b}*a*) =log

*(*_{c}*a*)log*(*_{c}*b*)See also

Write how to improve this tool