The log function also called a logarithm function which comes under most of the mathematical problems. The logarithmic function is used to reduce the complexity of the problems by reducing multiplication into addition operation and division into subtraction operation by using the properties of logarithmic functions. Here, the method to find the logarithm function is given with the help of value of log e.

In general, the logarithm is classified into two types. They are

• Common Logarithmic Function
• Natural Logarithmic Function

The log function with base 10 is called the “common logarithmic functions” and the log with base e is called the “natural logarithmic function”. The logarithmic function is defined by,

Where x is the logarithm of a number ‘b’ and ‘a’ is the base of the log function that could be either replaced by the value ‘e’ or ‘10’. The variable ‘a’ should be any positive number and that should not be equal to 1.

Value of e

The most important constant in the mathematical concept is exponential constant. The value of e is approximately equal to 2.7182818 which is rounded to the 7 digits. The exponential constant frequently occurs in mathematics whenever the exponential functions are involved.

How to calculate the value of Log e?

Now, let us discuss how to find the value of log e using common log function and natural log function.

Value of Log₁₀ e

The log function of e to the base 10 is denoted as “log₁₀ e”.

According to the definition of the logarithmic function, it is observed that

Base, a = 10 and 10^x = b

Therefore, the value of log e to the base 10 as follows

Log₁₀ e = log₁₀ (2.7182818) = 0.434294482

Log₁₀ e = 0.434294482

Where the value of e is 2.7182818.

Therefore, the value of log e to the base 10 is equal to 0.434294482

Value of log_e e

The natural log function of e is denoted as “log_e e”. It is also known as the log function of e to the base e. The natural log of e is also represented as ln(e)

According to the properties to the logarithmic function, The value of log_e e is given as 1.

Therefore,

Log_e e = 1 (or) ln(e)= 1

Because the value of e¹ = e.

Derivative of Log e

Since the natural log function to the base e (loge e) is equal to 1, The derivative of log e is equal to zero, because the derivative of any constant value is equal to zero.

Sample Problem

Question :

Solve e^x = 6.2

Solution:

Given : e^x = 6.2

Taking the natural log on both sides, it becomes

ln e^x = ln 6.2

Using the properties of log functions,

x ln e = ln 6.2

x = ln 6.2 / ln e

We know that, ln e = 1

Therefore,

x = ln 6.2 = 1.82455 (rounded to five digits)

So the value of x = 1.82455.

Download BYJU’S – The Learning App to get more information on logarithmic values and also watch interactive videos to clarify the doubts.