Answer
Verified
376.5k+ views
Hint: We first try to explain the use of logarithm and the general formulas of the logarithms. We prove it by contradiction where we assume ${{\log }_{b}}0=x$ and try to find the value of $x$ which is not possible due to the condition of $a,b>0$ for ${{\log }_{b}}a$.
Complete step by step answer:
The logarithm is used to convert a large or very small number into the understandable domain. For the theorem to work the usual conditions of logarithm will have to follow. If the base is not mentioned then the general solution for the base for logarithm is 10. But the base of $e$ is fixed for $\ln $. We also need to remember that for logarithm function there has to be a domain constraint.
For any ${{\log }_{b}}a$, the conditions are $a,b>0$ and $b\ne 1$.
We also prove it using contradiction. We assume ${{\log }_{b}}0=x$. We know the formula that if ${{\log }_{b}}a=p$ then ${{b}^{p}}=a$.
So, for ${{\log }_{b}}0=x$ we get ${{b}^{x}}=0$ which is possible only when $b=0$ which creates the contradiction.
Therefore, natural logarithm of 0 is not possible.
Note: Only logarithms for numbers between 0 and 10 were typically included in logarithm tables. To obtain the logarithm of some number outside of this range, the number was first written in scientific notation as the product of its significant digits and its exponential power.
Complete step by step answer:
The logarithm is used to convert a large or very small number into the understandable domain. For the theorem to work the usual conditions of logarithm will have to follow. If the base is not mentioned then the general solution for the base for logarithm is 10. But the base of $e$ is fixed for $\ln $. We also need to remember that for logarithm function there has to be a domain constraint.
For any ${{\log }_{b}}a$, the conditions are $a,b>0$ and $b\ne 1$.
We also prove it using contradiction. We assume ${{\log }_{b}}0=x$. We know the formula that if ${{\log }_{b}}a=p$ then ${{b}^{p}}=a$.
So, for ${{\log }_{b}}0=x$ we get ${{b}^{x}}=0$ which is possible only when $b=0$ which creates the contradiction.
Therefore, natural logarithm of 0 is not possible.
Note: Only logarithms for numbers between 0 and 10 were typically included in logarithm tables. To obtain the logarithm of some number outside of this range, the number was first written in scientific notation as the product of its significant digits and its exponential power.
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
Give 10 examples for herbs , shrubs , climbers , creepers
Change the following sentences into negative and interrogative class 10 english CBSE
Difference between Prokaryotic cell and Eukaryotic class 11 biology 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
Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE
Application to your principal for the character ce class 8 english CBSE
Write a letter to the principal requesting him to grant class 10 english CBSE