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.
The relationship between logarithms and exponents is described below:
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There are two types of logarithmic functions.
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
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.
We live in a log base 10 world we count and measure in powers of 10.
The value of log base 10 can be calculated either using 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.
The definition of the logarithmic function that is equal to 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 the value of e1=1.
The value of log 10 can be calculated either using common log function or the natural log function.
Let’s calculate the value of log of 10 using 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 log of 10 with base e is as follows,
loge10 or ln (10) = 2.302585
The values of log 1 to log 10 to the base 10 are as follows:
Question1) Solve for the value of ln e.
Solution) We can write ln e as logee.
Now, we can say that logee = x ,
Then, e=ex
By equating we get the value of x as 1.
Therefore, the value of logee = log e = 1.
Question 2) Based on the definition of logarithms, what is the value of log101000?
Solution) We know that, for any equation log10(y)=x,
10x=y.
Thus, in the question given above we are trying to determine what power of 10 is 1000.
So, the answer is 3.
Question 3) 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
\[\frac{xlog 7}{log 7} = \frac{3}{log 7}\]
Therefore, x = \[\frac{3}{log 7}\].
Question 4) Solve ln 4x =7
Solution) Taking exponential on both the sides to remove the log,
We get, \[e^{ln 4x} = e^{7}\]
\[4x = e^{7}\] > equation 1,
Putting the value of e = 2.7182 in equation 1,
\[4x = (2.7182)^{7}\]
\[x = \frac{(2.7182)^{7}}{4}\]
Therefore, x = 274.10.
Question 5) Solve ln 5x =12
Solution) Taking exponential on both the sides to remove the log,
We get, \[e^{ln 5x} = e^{12}\]
\[5x = e^{12}\] > equation 1
Putting the value of e = 2.7182 in equation 1,
\[5x = (2.7182)^{12}\]
\[x = \frac{(2.7182)^{12}}{5}\]
Therefore, x = 32539.20.
1. What is the Log 10 Value?
The value of log of 10 can be expressed in two ways either with base e or base 10. The value of log_{10}10 is equal to 1 whereas the value of loge10 or ln (10) is equal to 2.302585.
2. What is the Value of Logs?
The natural logarithm has its base equal to 2.718, as it is a simpler integral and derivative it is widely used in mathematics and physics.
3. 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 base equal to 10. The value of the common logarithm of 10 is equal to 1.
4. 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) 

ln(x) 
