What are Logarithmic Functions?
A logarithmic function is a function that is the inverse of an exponential function.
The purpose of the logarithm is to tell us about the exponent.
Logarithmic functions are used to explore the properties of exponential functions and are used to solve various exponential equations.
There are two types of logarithmic functions.
What Do You Mean by Common Logarithmic Function?
The common logarithmic function or common logarithm is the logarithm with a 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.
What Do You Mean by Natural Logarithmic Function?
The natural logarithmic function is the logarithm with a 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.
What is the Value of Log 10?
The value of log 10 can be represented either with base 10 or with base e.
The value of log1010 is equal to 1.
The value of loge10 which can also be written as ln (10) is 2.302585.
Note: The common log function is mostly used.
Logarithms
We live in a log base of 10 worlds, we count and measure in powers of 10.
How to Calculate the Value of Log 10?
The value of log base 10 can be calculated either using the common log function or the natural log function.
Let’s calculate the value of log 10 using common logarithm.,
The value of log1010 is equal to the log function of 10 to the base 10.
According to the definition of the logarithmic function, if logab =x, then ax=b.
Comparing log1010 with the definition, we have the base, a=10 and 10x=b,
Therefore, the value of log 10 is as follows,
We know that logaa=1.
Hence, the value of log 10 base 10 =1, this is because of the value of e1=1.
How to Calculate the Value of Log 10 Using Natural Log Function?
Let’s calculate the value of log of 10 using the natural logarithm.
The value of loge10 is equal to the log function of 10 to the base e.
It is also represented as ln (10).
Therefore, the value of the log of 10 with base e is as follows:
loge10 or ln (10) = 2.302585.
Here’s a Table Showing the Log 10 Value
The values of log 1 to log 10 to the base 10 are as follows:
Log Values From 1 to 10
Questions Using Log Value
Question 1: Solve for the value of ln e.
Solution:
The natural logarithm of a number x is defined as the base e logarithm of x:
ln(x) = loge(x)
So, the natural logarithm of e is the base e logarithm of e:
ln(e) = loge(e)
ln(e) is the number we should raise e to get e.
e1 = e.
So, the natural logarithm of e is equal to one.
ln(e) = loge(e) = 1.
Question 2: Express log101 = 0 in exponential form.
Solution: Given log101 = 0.
We know that logac=b ⇒ ab = c.
Therefore, 100 = 1.
Important Properties of Logarithms you need to know!
FAQs on Value of Log 10
1. What is the log 10 value?
The value of the log of 10 can be expressed in two ways either with base e or base 10. The value of log1010 is equal to 1 whereas the value of loge10 or ln (10) is equal to 2.302585.
2. What is the value of log base 10?
The value of log base 10, which is also known as the common logarithm, is the logarithm with a base equal to 10. The value of the common logarithm of 10 is equal to 1.
3. What is the opposite of log 10?
10 (x) is the inverse or the opposite of log10(x), which can also be denoted by log(x).
Here are the key differences between log and ln
Log(x)
Log(x) means the base 10 logarithm and can also be written as log10(x).
It tells you what power 10 must be raised in order to obtain the number x.
The inverse of log10(x) is 10x.
ln(x)
ln(x) means the base e logarithm and can also be written as loge(x).
ln(x) tells you what power e must be raised in order to obtain the number x.
The inverse of loge(x) is ex.
