
What is the difference between $ \log $ and $ \ln $ ?
Answer
411.6k+ 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
Master Class 11 Accountancy: Engaging Questions & Answers for Success

Glucose when reduced with HI and red Phosphorus gives class 11 chemistry CBSE

The highest possible oxidation states of Uranium and class 11 chemistry CBSE

Find the value of x if the mode of the following data class 11 maths CBSE

Which of the following can be used in the Friedel Crafts class 11 chemistry CBSE

A sphere of mass 40 kg is attracted by a second sphere class 11 physics CBSE

Trending doubts
10 examples of friction in our daily life

One Metric ton is equal to kg A 10000 B 1000 C 100 class 11 physics CBSE

Difference Between Prokaryotic Cells and Eukaryotic Cells

State and prove Bernoullis theorem class 11 physics CBSE

What organs are located on the left side of your body class 11 biology CBSE

The combining capacity of an element is known as i class 11 chemistry CBSE
