The value of log 4 to the base 10 is 0.6020. In this article, we are going to discuss the value of log 4 in terms of both natural logarithm and common logarithm in the logarithmic function. Logarithms are inverse of exponential functions.

Here is the value of log 4 with respect to base-10 and base-e.

How to calculate the value of Log 4?

Now, let us discuss how to find the value of log 4 using a common log function and natural log function. Also, find the log of 4 to the base 2 here.

Value of Log 4 to the base 10

The log function of 4 to the base 10 is denoted by “log₁₀ 4”.

According to the definition of the logarithmic function,

Base, a = 10 and 10^x = b

With the use of logarithm table, the value of log 4 to the base 10 is given by 0.6020

                                                            Log₁₀ 4 = 0.6020

Value of log 4 to the base e

The natural log function of 4 is denoted by “log_e 4”. It is also known as the log function of 4 to the base e. The representation of the natural log of 4 is ln(4).

Therefore,

log_e 4 = ln 4 = 0.60206 × 2.303 = 1.386

The value of log_e 4 is equal to 1.386.

                                                      log_e 4 = ln (4) = 1.386

Value of log 4 to the base 2

We can write the value of log 4 to the base 2 as:

log₂ 4 = log₂ (2)²

= 2 log₂ 2 (By power rule of logarithm)

Let us say, log₂ 2 = x

Now we can write the above expression in exponential form.

2 = 2^x

Since, 2¹ = 2

Thus, x = 1

Hence,

log₂ 4 = 2 log₂ 2 = 2 × 1 = 2

Therefore, the value of log 4 to the base 2 is equal to 2.

What is Logarithmic Function?

The log function or logarithm function is used to eliminate the exponential functions when the equation has exponential values. It is used in mathematical problems to simplify equations. The logarithmic function is defined by

if log_ab = x, then a^x = b.

Where,

x is the logarithm of a number ‘b.’

‘a’ is the base of the log function.

Note: The variable “a” must be any positive integer where it should not be equal to 1.

The classification of logarithmic functions is:

• Common Logarithmic Function – Base 10 log function
• Natural Logarithmic Function – Base e log function

If the base of the logarithmic function is other than 10 or e, convert it into either base e or base 10 using the base change rule.

Solved Examples on Value of log 4

Question: Solve log (2 ×4 ×6).

Solution:

Given that, log(2 ×4 ×6).

Using the properties of the logarithm (log a + log b = log ab)

It can be written as,

log(2 ×4 ×6) = log 2 + log 4 + log 6 ….(1)

We know that,

Log 2 = 0.3010

Log 4 = 0.6020

Log 6 =0.7781

Now substitute the log values in (1), we get

log(2 ×4 ×6) = 0.3010+0.6020 + 0.7781

log(2 ×4 ×6) = 1.6811

Therefore, the value of log(2 ×4 ×6) is 1.6811

Question 2: Evaluate 4 log₁₀ 4 – 10 = ?, up to three decimal places.

Solution: 4 log₁₀ 4 – 10 = 4 (0.602) – 10

= -7.592

Practice Questions

1. log₁₀ 4 + log₁₀ 2 = ?
2. 10 log₁₀ 4 – 5 log₁₀ 3 = ?

Related Articles

• Logarithmic Functions
• Value of Log e
• Value of Log 0
• Value of Log 10
• Value of Log Infinity

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