In Mathematics, most of the researchers use logarithms to transform multiplication and division problems into addition and subtraction problems before the concept of calculus came into the picture.
Logarithms are continuously used in Mathematics and Science as these both subjects contend with large numbers.
In this article, we will discuss the log 1 value (log 1 is equal to zero) and method to derive the value of log 1 through common logarithm functions and natural logarithm functions.
A logarithm is defined as the exponent or power to which a base must be raised to get some new number. It is a convenient approach to express large numbers.
Through logarithm, the multiplication of large numbers we can easily resolve speedily. Some common properties of logarithm which proved multiplication and division of logarithms can even be written in the form of logarithm of addition or subtraction.
Let’s take an example,
\[2^{3}\] = 8, where 3 is the logarithm of 8 to base 2 or can be written as 3= log28.
In a similar way, 10² = 100 which can be written as 2 = log₁₀100
Common or Briggsian logarithm is the logarithm with base 10.
Given below are the four basic properties of logarithm which would help you to resolve problems based on logarithm.
Logb(mn) = Logb m + Logb n This property of logarithm says that the multiplication of two logarithm values is equivalent to the addition of the individual logarithm. 
Logb (m/n) = Logb m  Logb n This property of logarithm says that the division of two logarithm values is equivalent to the subtraction of the individual logarithm. 
Logb (m^{n}) = n logbm The above property is known as the exponential rule of the logarithm. The logarithm of m along with the rational exponent is equivalent to the exponent times its logarithm. 
Logb m = loga m / loga When two numbers are divided with the same base, then the exponents will be subtracted. 
Before deriving Log 1 value, let us discuss logarithm functions and their classifications. A logarithm function is an inverse function to an exponential function. In Mathematics Logarithm can be expressed in the following way:
REPRESENTATION OF A LOGARITHM FUNCTION 
logab =x, then ax=b . 
If Logab = x, then ax=b
where, “x” = log of a number
“a” = base of a logarithm function.
Something you need to keep in mind! The variable “a” should always be a positive integer and not equals 1.
There are two types of logarithmic functions.
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Common Logarithmic Function or Common logarithm is the logarithm with base equal to 10.
It is also known as the decimal logarithm because of its base.
The common logarithm of x is denoted as log x.
Example: log 100 = 2 (Since 102= 100)
The Natural Logarithmic Function is the logarithm with base equal to the mathematical constant e.
The value of e which is a mathematical constant is approximately equal to 2.7182818.
The natural logarithm of x is written as logex.
Example: loge25= ln 25
From the definition of logarithm function,
We can write logab = x can be written in the form of an exponential form: ax = b
Now to find the value of log 1, here the base is not defined.
Let us consider the base of log 1 as 10.
Therefore, we can write log 1 as log10 1.≠
From the logarithm definition, the value of a = 10 and the value of b = 1.
Such that, log10 x = 1
Now by the logarithm rule, the above expression can be rewritten:
10x = 1
As we know, when any number is raised to the power 0 it is equal to 1.
Thus, 10 raised to the power 0 makes the above written expression true. So, 100 = 1
This is a condition for all the base value of log, where the base raised to the power 0 = 1
Therefore, we can conclude the value of log 1 is zero, where a can be any positive value (a≠1)
log101 = 0
Similarly, the natural logarithm value of 1( Ln 1) can be represented by,
Ln(b) = loge (b)
Therefore, Ln(1) = loge(1) or ex = 1
Therefore, e0 = 1
Hence, we can conclude that Ln(1) = loge(1) = 0
Value of log  
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 
In (1)  0 
In (2)  0.693147 
In (3)  1.098612 
In (4)  1.386294 
In (5)  1.609438 
In (6)  1.791759 
In (7)  1.94591 
In (8)  2.079442 
In (9)  2.197225 
In (10)  2.302585 
Question 1) Solve for y in log₂ y =6
Solution) The logarithm function of the above function can be written as 26 = y
Therefore, 25 =2 x 2 x 2 x 2 x 2 x 2 =64 or y = 64
Question 2) Calculate the value of x in 7x=1000.
Solution) Taking common logarithms on both the sides, and applying the property of the logarithm of a power,
7x=1000 can be written as,
7x=103
Log 7x= log 103
x log7 = 3 log 10
x log7 = 3 .1 (Using the log 10 value which is 1)
x log7 = 3
x log 7 log 7 = 3log 7
Therefore, x = 3log 7

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