Answer

Verified

384k+ 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.

Recently Updated Pages

what is the correct chronological order of the following class 10 social science CBSE

Which of the following was not the actual cause for class 10 social science CBSE

Which of the following statements is not correct A class 10 social science CBSE

Which of the following leaders was not present in the class 10 social science CBSE

Garampani Sanctuary is located at A Diphu Assam B Gangtok class 10 social science CBSE

Which one of the following places is not covered by class 10 social science CBSE

Trending doubts

Which are the Top 10 Largest Countries of the World?

What percentage of the solar systems mass is found class 8 physics CBSE

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

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

Why is there a time difference of about 5 hours between class 10 social science CBSE

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE