Value of Log 4

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. Here, the step-by-step is procedure is given to find the value of log 4.

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 the equations. The logarithmic function is defined by

if logab = x, then ax = 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 are:

  • 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.

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.

Value of Log10 4

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 10x = 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 ln (4) or loge 4

The natural log function of 4 is denoted by “loge 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)

The value of loge 4 is equal to 1.386294

                                                      loge 4 = ln (4) = 1.386294

Solved Problem

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

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