Difference Between Ln and Log: Something Worth Understanding

Difference Between Ln and Log: Something Worth Understanding

The Log is the term used to describe base 10, while it is defined as ln for base e. For instance, log 2 of base 2 can be recorded as log2, while the Log of base e is written as loge = ln (natural the Log).

The logarithm, which its value can define, is the basis that must be raised to get a number. It is known as the log number. It is its natural logarithm. “E” refers to the exponential formula. 

It was first realized by John Napierin in the 17th-century, who conceptualized the concept of logarithms. Let’s look at the definitions for Log and ln. After that, we will be able to discover the distinction between the two.

Before getting to the difference between Log and Ln, let us get to know the history.


The concept of logarithms was first established in the early seventeenth century. Later, scientists, navigators and engineers embraced the idea to calculate by using logarithmic tables.

The distinction from Log to ln is that the latter is defined as base 10, while ln is identified as the base of e. For instance, log2 from base 2 is denoted as log2, and Log of base e is represented as Log, i.e. loge = the word ln (natural log).

A natural logarithm could be called the power that is the base “e” needs to be raised to get a number known as the Log. The exponential function. It was first identified in 1771 by John Napier, who discovered and conceptualized the concept of logarithms. Before we get into the fundamental distinction between Log and ln, let’s look at the definition of Log and ln.

Log and Ln Definition

Log The logarithm is a term used in Maths. The logarithm is the reverse function of exponentiation. In simpler terms, the term “logarithm” is defined as a value to which a particular number needs to be raised to obtain a different number. 

It’s also known as the logarithm of the base 10 or the common logarithm. The most common version of a logarithm can be described as follows:

loga (y) = x

The form above is written in the following manner:

Ax = y

Rules of Logarithm:

 Four important rules or properties govern the logarithm.

(mn) = logb (mn)is logb M n = logb

(m/n) = logb (m/n)= logb m logbn

Logb (mn) = n logb m

Logb m = loga m/ loga b

Ln: Ln can be described as “the natural logarithm. It’s also known as the logarithm of base e. In this case, e is irrational, transcendental and is equivalent in value to 2.718281828459…

A natural logarithm (ln) is represented by loge x or ln.

Log vs ln

Understanding Log vs Ln isn’t that challenging, though.

The logarithm is an extremely valuable mathematic concept that can aid in the resolution of complex math issues. Logarithms, as a rule, are exponents. The capacity to which the base 10 has to be raised to arrive at the number is known as its log number. 

The capacity that the base e has to be raised to achieve an amount is known as the natural logarithm for the number. Many are confused about the difference between Log and ln. This article attempts to figure the distinctions between Log and the ln.

Log to the 10th base from 100 equals 2 as 10X10=100 and Log10100 = Log10102 = 2.

The base is 10; here, 10, 10 is the base of the number, and the logarithm is 2 100 refers to the number with a log of 2. Logarithms for those of the 10th base are referred to as common logarithms, also known as Log. 

In contrast, logarithms for the base (loge) (loge) are known as natural logarithms or the word ln (pronounced “lon).

For the distinction between Log and ln and how they relate to each other, look over these equations.

This is the root of the 10, which provides you with a particular number. We know that 10X10=100, which means that log 100 is 2. Similar to the above that lnx also is an exponent of the number e but does not equal 10, producing a different result.

We know that e = 2.18281828459, and the e X e value is 7.389056

Hence ln 7.389056 = 2

The difference between the two terms

We need to understand the precise distinction between Log and ln to solve the logarithmic problems with greater understanding, not just by calculating. 

It’s essential to have a deep understanding of these logarithmic functions, which could prove useful in understanding different concepts. The major differences between these two terms are outlined below.


Common logarithms can be found in a variety of uses in engineering and science. They are also referred to as Briggsian logarithms since, during the 1800s, British mathematician Henry Briggs introduced the concept. 

For instance, the acidity and alkalinity of a substance are measured in exponential units.

The Richter scale is used to measure earthquakes, and the decibel of sound is typically expressed as a logarithmic number. It’s so popular that it is possible to take it as Log the x, or common Log, even if there is no base written.


The natural logarithm of the numeric number is called the power or exponent, where ‘e’ must be raised to be equivalent with the number N. “E” represents the Napier constant, which is equivalent to 2.718281828.

Ln N = x, which is identical to N = e the value of.

Natural logarithms are used primarily in pure mathematics like calculus. The fundamental properties of natural logarithms are similar to those for all logarithms.

The Conclusion

John Napierin did a fabulous job, didn’t he? Hey, if you don’t know who it is, you certainly need to get through this article again! Sometimes, the explanations of Ln and Log get too complicated, which leads to a lot of confusion and frustration while understanding.

Marisa Lascala

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