## Log Definition

Log and Ln stand for Logarithm and Natural Log respectively. Logarithms are essential for solving equations where an unknown variable appears as the exponent of some other quantity. They are significant in many branches of mathematics and scientific subjects and are used to solve problems involving compound interest, which is broadly related to finance and economics.

In Mathematics, the logarithm can be defined as the inverse function of exponentiation.

In simpler words, the logarithm can be defined as a power to which a number must be raised in order to get any other number.

It is also known as the logarithm of base 10, or common logarithm.

The general form of a logarithm can be denoted as:

The above - given form can also be written as:

In this article we are going to discuss what is log, what is ln in math, Log and ln rules , the difference between Log and Ln x , difference between log and natural log and difference between log and ln graph.

Given below are the four basic properties of logarithm which will help you to easily solve problems based on logarithm.

### Properties of Logarithm

### Log Value from 1 to 10

### What is Ln in Maths?

Ln is called the natural logarithm. It is also called the logarithm of the base e. Here, the constant e denotes a number that is a transcendental number and an irrational which is approximately equal to the value 2.71828182845. The natural logarithm (ln) can be represented as ln x or \[\log_{e}x\].

### Let’s go Through the Different Rules of Ln

We have discussed the log and ln rules above.

Log values from 1 to 10 to the base e are given below-

### Table Showing Ln Values From 1 to 10.

### Difference Between Log and ln Graph

These graphs will show you the difference between log and ln graph.

(Images will be uploaded soon)

Let’s discuss some of the key differences Between Log and Ln:

To solve logarithmic problems,one must know the difference between log and natural log. Having a key understanding of the exponential functions can also prove helpful in understanding different concepts. Some of the important difference between Log and natural log are given below in a tabular form:

### Difference Between Log and Ln x

### Questions to be Solved:

Question 1) Solve for y in log₂ y =6

Solution) The logarithm function of the above function can be written as 26 = y

Therefore, \[2^{6}\] = 2 x 2 x 2 x 2 x 2 x 2 =64 or y = 64

Question 2) Simplify log(98).

Answer) We will use the Log and ln rules we have discussed. Since, we know that the number 98 is not a power of 10 (the way that 100 was), So we can find the value by plugging this into a calculator, remembering to use the "LOG" key (not the "LN" key), and we get log(98) = 1.99122607569..., or log(98) = 1.99, rounded to two decimal places.

### Fun Facts

The first man to bring the concept of Logarithm in modern times was the German Mathematician, Michael Stifel (around the year 1487 -1567).

The logarithm with base 10 is called as common or Briggsian, logarithms and can also be written as log n. They are usually written without base.

## FAQs on Difference Between Log and Ln for JEE Main 2024

**1. Is Log Base 10 the Same as Ln?**

A logarithm is a number that is written as \[\log_{b}(x)\], and it is equal to the number that we need to raise b to in order to get x. In mathematics, some logarithms show up more often than others, and we classify these logarithms as special types of logarithms by the value of their base.

**2. Does Ln Mean Log?**

ln(x) means the base e logarithm; it can also be written as \[\log _{e}(x).\ln (x)\].

**3. How should Log be used?**

When logarithms are added, they should be multiplied. Let’s learn about it through an example:

\[\log_{2}{x}+ \log_{2}{y}= \log_{2}{xy}\]

Another example is log2128. We may not know what 2 to whose power is 128 from the top of the head so basically, we can split this into two smaller logarithms using this property. Here is how it’s split up.

\[\log_{2}{128} = \log_{2}{32} + \log_{2}{4}\]

After finding the logs through the exponents, this is our final answer.

\[\log_{2}{128} = \log_{2}{32} + \log_{2}{4}\]

\[\log_{2}{128} = 5+2\]

\[\log_{2}{128} = 7\]

This is the quickest and smartest way of solving a logarithm. You should keep in mind that this method can be used only when the bases of both the logarithms are similar.