How to Calculate the Value of Log 3?
To calculate the value of log 3 there are two methods i.e.,
- Using Log Table
- Using Taylor Series
Discuss these methods as follows:
Using a Log Table
For any number without any decimal, it is very easy to find the value using a log table as we can see
Step 1: Find a Log Table with base 10.
Step 2: Locate the row corresponding to the mantissa (3).
Step 3: Identify the column for the characteristic (whole number part) which is 0 here.
Step 4: The intersection of row and column provides the logarithm value (log 3 ≈ 0.4771).
Read More about Log Table.
Using Taylor Series
To calculate the value of logarithm of 3 using Taylor series expansion, you can use the Taylor series expansion of the natural logarithm function. The natural logarithm of x can be represented as:
ln(x) = (x – 1) – (1/2)(x – 1)2 + (1/3)(x – 1)3 – (1/4)(x – 1)4 + . . .
To calculate ln(3), you would plug in x = 3 into this series expansion.
ln(3) ≈ (3 – 1) – (1/2)(3 – 1)2 + (1/3)(3 – 1)3 – (1/4)(3 – 1)4 + . . .
⇒ ln(3) ≈ 2 – 1 + 2/3 – 1/2
⇒ ln(3) ≈ 1 + 4/6 – 3/6 ≈ 1 + 1/6 ≈ 1.166666. . .
As we know log x = ln x/ln 10, and ln 10 = 2.3026
Thus, log 3 = ln 3/2.3026 ≈ 0.51
Note: The higher the number of terms taken from the series expansion, more accurate is the result.
Value of log 3
Value of log(3) is 0.4771 in base 10 (common logarithm) and log(3) is 1.098612 in base e (natural logarithm) . A logarithm is a mathematical function that expresses the power to which a base must be raised to produce a given number or we can say it is a different way to represent the exponent.