Value of Log 10

Value of log 10 is 1 whereas the value of ln 10 is approximately 2.3026. The logarithm base 10 is denoted as log and is called a common logarithm whereas a logarithm with base e is represented as ln and is called a natural logarithm. In this article, we are going to learn what is the value of log 10, how the value is derived, and many more things about log 10.

👁 Value-of-Log-10

What is the Value of Log 10?

Value of log 10 in any base is the number which when raised to the base as power is equal to 10 i.e.,

log_b 10 = x ⇒ b^x = 10

For different bases value of log 10 is different, some of the most common value of log 10 are:

• Value of log 10 (Base e)
• Value of log 10 (base 10)

Let's discuss these values in detail as follows.

Value of log 10 (Base e)

Vallue of log_e 10 is approximately equal to 2.3026 or in the exponent form we can say that e^2.3026 = 10. Mathematically it is written as

log_e 10 = 2.3026

OR

ln 10 = 2.3026

Value of log 10 (base 10)

Value of log 10 is 1 as the base of the common logarithm is 10 and log_a a = 1. Also, as log is an inverse function of exponents we can also explain the same thing using the exponent i.e., as 10¹ = 10 thus the value of log₁₀ 10 is 1.

Value of Log 10 in Different Bases

Values of Log 10 in different bases in given in the following table:

Base	LogBase 10
2	3.3219
e	2.3026
3	2.0956
4	1.6021
5	1.4307
10	1

Value of Log 10 Calculator

Try the following calculator tool to calculate the value of Log 10:

How to Calculate the Value of Log 10?

Let's see to calculate the value of Log 10 using base 10:

• Using Log Formula
• Using a Log Table
• Using Taylor Series Expansion

Using Log Formula

log_ba = log_ca / log_cb

As we know, the logarithm base 10 of a number x is the exponent to which 10 must be raised to obtain x. So, In this case: Here x is also 10 and base is also 10.

Then: According to definition, (10)1 = 10.Hence the value of Log₁₀ 10 = 1.

Using a Log Table

Calculating the value of a whole number is straightforward with a log table.

Step 1: Refer to a Log Table with base 10. (Log Table PDF)

Step 2: Find the row for the mantissa (10).

Step 3: Identify the column for the characteristic (0).

Step 4: The intersection of both row and column in log table is the value log 10 i.e., 1.

Read More about Log Table.

Using Taylor Series Expansion

The Taylor series expansion can be used to find the value of log 10. we can use the Taylor series expansion for ln x:

ln( 1 + x ) = x - x²/2 + x³/3 - x⁴/4 + ....

We can put x=9, to get the value of ln 10,

ln( 1 + 9 ) = 9 - 9²/2 + 9³/3 - 9⁴/4 + . . .

After solving this series, we get the value of log 10 which is a approximate value.

Note: Higher the number of terms taken, the closest the value of expansion to log 10.

Read More about Taylor Series.

Important Points for Value of Log 10

• The value of log₁₀10 is equal to 1 .
• The value of log_e10 is equal to 0.4342944.

Read More,

• What is a Logarithm?
• Logarithm Rules
• Antilog Table

Sample Examples on Value of Log 10

Example 1: Find the Derivative of log_e10?

Solution:

We know that log₁₀10 = 1

Hence, d/dx(log₁₀10) = d/dx(1) = 0

Example 2: What is the value of log₁₀ 100?

Solution:

log₁₀100 = log₁₀(10)2

Using Log Formula

log₁₀(10)2 = 2×log₁₀(10) = 2 × 1 = 2

Example 3: What is the value of q in log₁₀ (q-2) = 1 ?

Solution:

log₁₀(q-2) = 1

⇒ 101 = q-2

⇒ 10 = q-2

⇒ p = 10 + 2 = 12

Practice Questions on Value of Log 10

Q1: If 10^x = 100000, Find x.

Q2: Given that log₁₀(z – 2) = 6, find z.

Q3: Find the value of √10.