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 “log_b(x)” and is defined as:

log_b(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.

log_e4 ≈ 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 3^1.2619 = 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 (a^b) = 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,

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

Solved Examples on Value of Log 4

Example 1: Solve for value of log 4².

Solution:

As we know, log a^b = b × log a

Therefore, log 4² = 2 × log 4 ≈ 2 × 0.6021 = 1.2042

Example 2: If 10^x = 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 4^y = 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.