Value of log 3
Last Updated :
07 Mar, 2024
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.
What is Logarithm?
A logarithm, denoted as “log,” is a mathematical function that represents the exponent to which a specified base must be raised to obtain a given number. In other words, it’s a way of expressing an exponent.
The logarithm of a number “x” to the base “b” is denoted as “logb(x)” and is defined as:
logb(x) = y
Value of log 3 base 10
Log base 10 is also called a common logarithm. The value of log 3 base 10 is given below:
log103 = log 3 ≈ 1.098612
Value of log 3 base e
Log base e is also called Natural Logarithm. The value of log 3 base e is given below:
loge3 = ln 3 ≈ 0.4771
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.
Conclusion
Log 3 represents the power to which the base 10 must be raised to produce the number 3.It is a mathematical concept which is widely used in various fields such as engineering, mathematics and science. In this article we discussed about what is logarithm , the value of log 3 base 10 and base e. We also discussed how we can calculate the value of log 3 by using log table and using logarithmic formulaes.
Sample Problems on Value of Log 3
Problem 1: Find the value of log 33.
Solution:
log ab = b × log a
log 33 = 3 × log 3
= 3× 0.4471
≈ 1.4313
Problem 2: find the value of x, 10x = 3 ?
Solution:
10x = 3
Taking log base 10 both sides, we get
log1010x = log103
⇒ x log1010 = log103
⇒ x = log10 3 [log1010 = 1]
⇒ x = log10 3 / log10 10
⇒ x = 0.4471/ 1
⇒ x = 0.4471
Value of Log 3: FAQs
What is Logarithm?
A logarithm is a mathematical function that reverses the exponentiation operation. It is a way to express the power to which a number must be raised to obtain a given value.
What is the Value of log 3?
log 3 = log10 3 = 0.4471
What is the Value of ln 3?
The value of loge 3 is 1.098612.
What is Antilogarithm?
An antilogarithm, often referred to as an antilog, is the inverse of a logarithm.
Write the value of antilog 3.
antilog 3 (base 10) = 1000
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