Value of Log 10

The log function also called a logarithm function which is used in most of the mathematical problem that contains exponential functions. If the equation contains exponential values, log functions are used to remove the exponential values and vice versa. In order to reduce the complexity of the problems, the properties of logarithmic functions are used to reduce multiplication operation to addition operation and division operation to the subtraction operation. The logarithmic function is generally classified into two types, namely

  • Common Logarithmic Function
  • Natural Logarithmic Function

The log function with base 10 is called the common logarithmic functions and the logarithm with base e is called the natural logarithmic function. Mostly the common log function is used. If the logarithmic functions contain different bases other than 10 and e, it is converted using the change of base rule.

The logarithmic function is defined by,

if logab = x, then ax = b.

Where x is the logarithm of a number ‘b’ and ‘a’ is the base of the log function that could be either replaced by the value ‘e’ or ‘10’. The variable ‘a’ should be any positive number and that should not be equal to 1.

How to calculate the value of Log 10?

Now, let us discuss how to find the value of 10 using a common log function and natural log function.

Value of Log10 10

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

According to the definition of the logarithmic function, it is observed that

Base, a = 10 and 10x = b

Therefore, the value of log 10 to the base 10 as follows

From the properties of the logarithmic function, we know that loga a = 1

The value of log10 10 is given as 1.

Log10 10 = 1

Because the value of e1 = e.

Value of loge 10

The natural log function of 10 is denoted as “loge 10”. It is also known as the log function of 10 to the base e. The natural log of 10 is also represented as ln(10)

The value of loge 10 is equal to 2.302585

loge 10 = ln (10) = 2.302585

Log Values from 1 to 10

Some of the values of log functions to the base 10 from the value of log 1 to the value of log 10 are as follows:

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   

Sample Problem

Question :

Solve ln 3x = 5

Solution:

Given : ln 3x = 5

Take exponential on both sides to remove the natural log functions, it becomes

eln 3x = e5

3x = e5

3x = (2.7182)5

x=(2.7182)5/ 3

x=49.46

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

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