Types of Logarithm
We usually deal with two kinds of logarithms:
- Common logarithm
- Natural logarithm
Note: There can be a logarithm with any real number as its base but these two i.e., common and natural logarithm, are the most common and standard ones.
Let’s discuss these types in detail.
Common Logarithm
A common logarithm, often known as log base 10 or simply log, is a mathematical function that represents the exponent to which a given number must be increased in order to reach a given number. It calculates the power of ten necessary to get a certain number.
For example, log10(100) equals 2, because 10 raised to the power of 2 equals 100. The common logarithm of 100 in this case is 2, showing that 102 = 100. Common logarithms are used in many sectors, including science, engineering, and finance, to simplify huge number representations and help in computations requiring powers of 10.
Natural Logarithm
The natural logarithm is a mathematical function that expresses the logarithm to the base ‘e’ (Euler’s number, roughly 2.71828). It is the inverse of the exponential function and represents the amount of time required for a quantity to increase or decrease by a constant factor.
For example, ln (10) ≈ 2.30259 means that e multiplied by 2.30259 equals 10. The natural logarithm is used in many domains, including mathematics, physics, and finance, to describe phenomena that display exponential growth or decay, such as population expansion, radioactive decay, and compound interest computations.
Log Rules
Logarithm Rules or Log Rules are critical for simplifying complicated formulations that include logarithmic functions. Log Rules make it easier to calculate and manipulate logarithms in a variety of mathematical and scientific applications. Out of all these log rules, three of the most common are product rule, quotient rule, and power rule. Other than these, we have many rules of the logarithm, which we will discuss further in the article. This article explores, all the rules for logs including derivative and integral, in detail with the Logarithm Rules Examples. So, let’s start learning about all the rules logarithms have.
Table of Content
- What are Log Rules?
- Types of Logarithm
- List of Logarithm Rules
- Natural Log Rules
- Applications of Logarithm
- Product Rule of Logarithms
- Logarithm Power Rule
- Quotient Rule of Logarithms
- Solved examples of Log Rules
- Practise Questions on Log Rules