A Guide to Logarithm Rules

A logarithm is an exponent to a certain base number and must be raised or multiplied by itself to generate another number. Logarithm rules and logarithm properties are essential for understanding logarithm in a better way. It is an opposite function of exponentiation. Mathematics and science are constantly dealing with large power of number sets, while logarithm is the best way to treat calculations. Logarithms are just inverse process exponentiation that helps in calculation, navigation, science, and technology.  

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This article will take you through a better understanding of logarithm in mathematics, such as logarithm rules and logarithm properties. Here you can find detailed explanations with examples.  

Logarithm Definition 

Logarithm tells how many times one number or the base number needs to multiply by itself to produce another new number.  

Examples:  

2*2*2=8  

In logarithm, it can be written as,  

log2(8) =3 

This means the base number 2 needs to multiply by itself 3 times to get the newly produced number 8.  

So that logarithm can be concluded as,  

Logb x = n or bn = x 

Logarithm Rules and Properties 

In Math, there are four major logarithm rules Product rule, Quotient rule, Power rule and Change of base rule. There are two more rules zero rule and identity rule.  

• Product rule: logb mn = logb m + logb n. 

It indicates that the logarithm of the product is the total of the factors.  

• Quotient rule: logb m/n = logb m - logb n. 

It points out the difference in the logarithm. 

• Power rule: logb mn = n logb m. 

It shows the logarithm of a number raised to an exponent, which is the power times logarithm of the numbers.  

• Change of base rule: loga b = (logc b) / (logc a). 

It allows to change of a base of the algorithm to a different base.  

Moreover, the zero rules algorithm always produces zero, no matter what the base number is. The identity rules refer to a base to itself will be always 1.  

Different Types of Logarithms  

Generally, there are two different types of logarithms, such as common logarithms and natural logarithms.  

• Common logarithms- It is represented as log10 or simply log. The common logarithm defines how many times we need to multiply 10 to get the desired outcome.  

• Natural logarithm- It is represented as In or loge. The natural logarithm defines how many times we need to multiply e to get the required number.  

To sum up, nowadays logarithms are very common in the field of science and technology. Logarithm calculators are also in use making calculation easier. Logarithm rules make calculations appropriate so that scientists can blindly trust them. It helps to measure noise pollution, intensity of earthquakes, and radioactivity and acidic reactions in science.  

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FAQ (Frequently Asked Question) 

 Q.1. What are the different types of logarithms?  

Ans- There are two types of logarithms, common logarithm and natural logarithm.  

Q.2. How to calculate logarithm?  

Ans- The formula is log base x = y, x is the base number and y is the power of the number.  

Q.3. What is the law of logarithm?  

Ans- The law is log A + log B = log AB. 

Q.4. What type of Math is a logarithm?  

Ans- Logarithm is considered as arithmetic.  

Q.5. What are the common uses of logarithm?  

Ans- It is mostly used in science and technology to calculate complex equations.

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