Value of Log 2

The log function or logarithm function is used in most mathematical problems that hold the exponential functions. Log functions are used to eliminate the exponential functions when the equation includes exponential values.

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” should be any positive integer, and it should not equal to 1.

The classification of logarithmic functions are:

  • Common Logarithmic Function – Log function with base 10
  • Natural Logarithmic Function – Log function with base e

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

How to calculate the value of Log 2?

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

Value of Log10 2

The log function of 2 to the base 10 is denoted by “log10 2”.

According to the definition of the logarithmic function,

Base, a = 10 and 10x = b

With the use of logarithm table, the value of log 2 to the base 10 is given by 0.3010

Log10 2 = 0.3010

Value of ln (2) or loge 2

The natural log function of 2 is denoted by “loge 2”. It is also known as the log function of 2 to the base e. The representation of natural log of 2 is ln(2)

The value of loge 2 is equal to 0.693147

loge 2 = ln (2) = 0.693147

Log Values from 1 to 10

The values from log 1 to 10 to the base 10 are:

Log 1

0

Log 2

0.3010

Log 3

0.4771

Log 4

0.6020

Log 5

0.6989

Log 6

0.7781

Log 7

0.8450

Log 8

0.9030

Log 9

0.9542

Log 10

1

Ln Values from 1 to 10

The values from log 1 to 10 to the base e are:

ln (1)

0

ln (2)

0.693147

ln (3)

1.098612

ln (4)

1.386294

ln (5)

1.609438

ln (6)

1.791759

ln (7)

1.94591

ln (8)

2.079442

ln (9)

2.197225

ln (10)

2.302585

Solved Problem

Question :

Solve log (x-2) – log (2x -3) = log 2

Solution:

Given that, log (x-2) +log (2x -3) = log 2

Using the properties of the logarithm (log a – log b = log a/b)

It can be written as,

log ((x-2)/(2x-3)) = log 2

Since the base of the log function is 10, it becomes

⇒10log((x-2)/(2x-3)) = 10log(2)

⇒(x-2)/(2x-3) = 2

Bring 2x-3 to R.H.S

⇒(x-2)= 2(2x-3)

⇒x-2=4x-6

⇒x-4x =-6+2

⇒-3x = -4

⇒ x = 4/3

Therefore, the value of x is 4/3.

To learn the values of natural log and common log, register with BYU’S – The Learning App and also watch interactive videos to clarify the doubts.