Value of Log 4
Value of log(4) is 1.3863 in base e (natural logarithm) and 0.6021 in base 10 (common logarithm). 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.
In this article, we will learn about the value of log 4 in different base such as 10, e, 3, and 2 and also learn about the methods from which we can find the value of log 4.
What is Logarithm?
A logarithm, often abbreviated 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 4
Values of log 4 in different bases represent the number needed to raise the base to the power to obtain 4 as the result.
For instance, in base 10, the value of log 4 is approximately 0.60, implying that 10 to the power of 0.60 is approximately equal to 4. Similarly, in the case of log base 4, it signifies the power to which 4 must be raised to obtain a given result.
Value of log 4 (Base e)
Calculating the value of log 4 base e involves determining the exponent to which the mathematical constant e must be raised to equal 4. It determines the exponent to which the mathematical constant e must be raised to yield the value 4.
loge4 ≈ 1.3863
Value of log 4 (Base 10)
The value of log 4 base 10 is obtained by identifying the power to which the base 10 must be raised to equal 4
log104 ≈ 0.6021
Value of log 4 (Base 2)
The value of log base 2 of 4 is 2, as 2 raised to the power of 2 equals 4 (22 = 4) which is represented as
log2 (4) = 2
Value of log 4 (Base 3)
The value of log base 3 of 4 is approximately 1.2619 which represents 31.2619 = 4. This value of log 4 in base 3 can be represented as
log3 (4) ≈ 1.2618
Value of Log 4 Calculator
Try the following calculator to find the value of Log 4:
How to Calculate the Value of log 4?
To calculate the value of log 4 there are two methods i.e.,
- Using Log Table
- Using Logarithmic Formulas
Discuss these methods as follows:
Using a Log Table
For any number without any decimal it is very easy to find the value using log table as we can see
Step 1: Find a Log Table with base 10. (Refer for Log Table PDF)
Step 2: Locate the row corresponding to the mantissa (4).
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 4 ≈ 0.6021).
Read More about Log Table.
Using Logarithmic Formulas
We can calculate the value of log 4, using the value of log 2 and the basic logarithm formulas as follows:
log 4 = log(22) = 2 log 2 [Using log (ab) = b log a]
Value of log 2 ≈ 0.3010
Thus, log 4 ≈ 2 × 0.3010 = 0.6020
Points to Remember about Log 4
Some of the most important points related to log 4 are:
- Value of log 4 is 0.6021 (common logarithm).
- Value of ln 4 is 1.3863 (natural logarithm).
- Value of log4 4 is 1.
Read More,
Solved Examples on Value of Log 4
Example 1: Solve for value of log 4².
Solution:
As we know, log ab = b × log a
Therefore, log 42 = 2 × log 4 ≈ 2 × 0.6021 = 1.2042
Example 2: If 10x = 4, find the value of x?
Solution:
x = log104
⇒ x = log104 / log1010
⇒ x = 0.6021 / 1
⇒ x = 0.6021
Example 3: Solve for y in the equation 4y = 64?
Solution:
y = log464
⇒ y = log1064 / log104
⇒ y = 1.8062 / 0.6021
⇒ y = 3
Example 4: If log4x= 3, find the value of x?
Solution:
Rewrite the equation in exponential form: 43 = x
Therefore, x = 4 * 4 * 4 = 64
Example 5: Solve for z in the equation 4(2z-1) = 1?
Solution:
Any non-zero number raised to the power of 0 equals 1.
Therefore, 2z – 1 = 0
Solving for z, we get z = 1/2
Practice Problems on value of log 4
Problem 1: Evaluate log48?
Problem 2: Find the exact value of log 16?
Problem 3: Simplify log(43 × 42)?
Problem 4: Determine the value of log√64?
Problem 5: Simplify log 4-3?
Problem 6: Calculate the value of log(4 × 4)?
FAQs on Value of Log 4
Define Logarithm.
A logarithm is the exponent to which a specific base must be raised to obtain a given number. It represents the power to which a base is raised to produce a given result.
What is the Value of Log 4 in Base 10?
The value of log 4 in base 10 is approximately 0.6021.
What is the Value of Log 4 in Base e?
The value of log 4 in base e (natural logarithm) is approximately 1.3863.
What is the Value of Log 4 in Base 2?
The value of log 4 in base 2 is exactly 2, because 22 equals 4.
What is the Value of Antilog 4?
The antilog of 4 is 10,000. In other words, 104 equals 10,000.
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