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.

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.