Rules of Logarithm | Log Rules
The common properties or rules of Log are :
- Product Rule
- Division Rule
- Power Rule
- Change of Base Rule
- Base Switch Rule
- Equality of Log
- Number raised to Log Power
- Negative Log Rule
Read in Detail: Logarithm Rules | List of all the Log Rules with Examples
Product Rule of Log
Product rule of log states that if log is applied to the product of two numbers then it is equal to the sum of the individual logarithmic values of the numbers. The expression can be given as:
logxab = logxa + logxb
Example: loga10 = loga(5 ✕ 2) = loga5 + loga2
Quotient Rule of Log
Quotient Rule of log states that if log is applied to the quotient of two numbers then it is equal to the difference of the individual logarithmic value of the numbers. The expression can be given as:
logxa/b = logxa – logxb
Example: logx2 = logx(10/5) = logx10 – logx5
Power Rule of Log
Power Rule of log states that if the argument is raised to some power then the solution of logarithmic expression is given by the power of the argument multiplied by the log value of the argument. The expression can be given as:
logxab = b.logxa
Change of Base Rule
In logarithm, the base can be changed in the following way
logxa = logya/logyb
logxa.logyb = logya
Base Switch Rule
This log property states that Base and argument can be switched in the following manner
logxa = 1/logax
Equality of Logarithm
Equality of logarithm property states that if
logxa = logxb then a = b
Number Raised to Log
If a number is raised to log which has the same base as the number then the result of the expression is the argument. This can be expressed as
Negative Log Rule
The Negative Log Property states that if the logarithmic expression is of the form -logxa then we can convert it into a positive form by taking the reciprocal of the argument or by taking the reciprocal of the base as
-logxa = logx(1/a) = log1/xa
Articles related to Logarithms:
Apart from the above-mentioned properties, there are some other properties of Log. Using these properties we can directly put their values in any equation. These properties are mentioned below:
Log 1
This property of log states that the value of Log 1 is always zero, no matter what the base is. This is because any number raised to power zero is 1. Hence, Log 1 = 0.
Logaa
This Property of log states that if the base and augment of a logarithm are the same then the logarithm of that number is 1. This is because any number raised to power 1 results in the number itself. Hence,
- ln e = logee = 1
- log1010 = 1
- log22 = 1
Log 0
This rule states that the log of zero is not defined as there is no such number when raised to any power that results in zero. Hence, log 0 = Not defined.
Logarithm – Definition, Rules , Properties and Examples
A Logarithm is a mathematical function that represents the exponent to which a fixed number, known as the base, must be raised to produce a given number. In other words, it is the inverse operation of exponentiation.
Logarithms are widely used in science, engineering, and mathematics for dealing with very large or very small numbers, as they allow for easier manipulation and comparison of exponential rates of growth or decay. They are foundational in fields such as acoustics, electronics, and in the analysis of algorithms, where they help in understanding the complexity and performance.
Let’s learn logarithms in detail, including logarithmic functions, Logarithm rules, Logarithm properties, Logarithm graphs, and Logarithm examples.
Table of Content
- What is Logarithm?
- Logarithms Meaning
- Exponential to Log Form
- Log to Exponential Form
- Definition of Logarithm | Log Definition
- Logarithm Types
- Common Logarithm
- Natural Logarithm
- Difference between Log and ln | log vs ln
- Rules of Logarithm | Log Rules
- Product Rule of Log
- Quotient Rule of Log
- Power Rule of Log
- Change of Base Rule
- Base Switch Rule
- Equality of Logarithm
- Number Raised to Log
- Negative Log Rule
- Articles related to Logarithms:
- Log 1
- Logaa
- Log 0
- Logarithmic Function
- Expanding and Condensing Logarithm
- Expanding Log
- Condensing Log
- Logarithmic Formulas
- Log Calculator
- Log Table
- Anti Log Table
- Logarithmic Graph
- Properties of Logarithmic Graph
- Solved Examples on Logarithm
- Practice Questions on Logarithm
Contact Us