The value of log can be either with base 10 or with base e. The log₁₀ 10 value is 1 while the value of log_e 10 or ln(10) is 2.302585.

What is the Value of Log 10?

To recall, the logarithmic function is generally classified into two types, namely

• Common Logarithmic Function
• Natural Logarithmic Function

The log function with base 10 is called the common logarithmic functions, and the logarithm with base e is called the natural logarithmic function. Mostly the common log function is used. If the logarithmic functions contain different bases other than 10 and e, it is converted using the change of base rule.

The logarithmic function is defined by,

if log_ab = x, then a^x = b.

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.

In this article, let us discuss how to find the value of log 10 to the base 10 and base e in detail.

Also, check out key differences between log and ln here.

How to Calculate Log 10 value?

Now, let us discuss how to find the value of 10 using a common log function and natural log function.

Value of Log₁₀ 10

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

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

Base, a = 10 and 10^x = b

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

From the properties of the logarithmic function, we know that log_a a = 1

The value of log₁₀ 10 is given as 1.

Log₁₀ 10 = 1

Because the value of e¹ = e.

Value of log_e 10

The natural log function of 10 is denoted as “log_e 10”. It is also known as the log function of 10 to the base e. The natural log of 10 is also represented as ln(10)

The value of log_e 10 is equal to 2.302585

log_e 10 = ln (10) = 2.302585

Log Values from 1 to 10

Some of the values of log functions to the base 10 from the value of log 1 to the value of log 10 are as follows:

Example Question Using Log Value

Question: Solve ln 3x = 5

Solution:

Given : ln 3x = 5

Take exponential on both sides to remove the natural log functions, it becomes

e^{ln 3x} = e⁵

3x = e⁵

3x = (2.7182)⁵

x=(2.7182)⁵/ 3

x=49.46

To know about the values of natural log and common log, register with BYU’S – The Learning App and also watch interactive videos to clarify the doubts.