Answer
Verified
379.2k+ views
Hint: In the above question, we are required to point out a difference between the given two logarithmic functions with different bases. So to solve this question requires theoretical knowledge regarding the logarithmic functions and its base. A logarithm function is the inverse of an exponential function (a function in which one term is raised to the power of another term is known as an exponential function). An exponential function is of the form $ a = {x^y} $ , so the logarithm function being the inverse of the exponential function is of the form $ y = {\log _x}a $ .
Complete step-by-step answer:
In the given problem, we have to differentiate between the two mathematical functions $ \log $ and $ \ln $ provided to us in the problem itself.
So, the $ \log $ function is the logarithm function with base being equal to $ 10 $ . So, it can also be written as $ {\log _{10}} $ to be clear and understandable.
On the other hand, the $ \ln $ function is the logarithmic function with base being equal to e, where e is the Euler’s number or constant. So, it can be written as $ {\log _e} $ to be clear. This $ \ln $ function is also called a natural logarithm function.
The standard base of logarithm functions is 10, that is, if we are given a function without any base like $ \log x $ then we take the base as 10.
But, when we are specifically given the base of the logarithm function as e, we have to take the function as $ \ln x $ .
Note: So, both the functions given to us in the question are logarithmic functions just with different bases. We should know when to use which function as it can create a misunderstanding and confusion otherwise. We should keep in mind an important rule that the base of the logarithm functions involved should be the same in all the calculations in order to apply any property of logarithm. There are several laws of the logarithm that make the calculations easier and help us evaluate the logarithm functions.
Complete step-by-step answer:
In the given problem, we have to differentiate between the two mathematical functions $ \log $ and $ \ln $ provided to us in the problem itself.
So, the $ \log $ function is the logarithm function with base being equal to $ 10 $ . So, it can also be written as $ {\log _{10}} $ to be clear and understandable.
On the other hand, the $ \ln $ function is the logarithmic function with base being equal to e, where e is the Euler’s number or constant. So, it can be written as $ {\log _e} $ to be clear. This $ \ln $ function is also called a natural logarithm function.
The standard base of logarithm functions is 10, that is, if we are given a function without any base like $ \log x $ then we take the base as 10.
But, when we are specifically given the base of the logarithm function as e, we have to take the function as $ \ln x $ .
Note: So, both the functions given to us in the question are logarithmic functions just with different bases. We should know when to use which function as it can create a misunderstanding and confusion otherwise. We should keep in mind an important rule that the base of the logarithm functions involved should be the same in all the calculations in order to apply any property of logarithm. There are several laws of the logarithm that make the calculations easier and help us evaluate the logarithm functions.
Recently Updated Pages
How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE
Mark and label the given geoinformation on the outline class 11 social science CBSE
When people say No pun intended what does that mea class 8 english CBSE
Name the states which share their boundary with Indias class 9 social science CBSE
Give an account of the Northern Plains of India class 9 social science CBSE
Change the following sentences into negative and interrogative class 10 english CBSE
Trending doubts
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths
In Indian rupees 1 trillion is equal to how many c class 8 maths CBSE
Which are the Top 10 Largest Countries of the World?
How do you graph the function fx 4x class 9 maths CBSE
Give 10 examples for herbs , shrubs , climbers , creepers
Difference Between Plant Cell and Animal Cell
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
Why is there a time difference of about 5 hours between class 10 social science CBSE