Courses
Courses for Kids
Free study material
Offline Centres
More Last updated date: 04th Dec 2023
Total views: 281.1k
Views today: 7.81k

# Find the natural logarithm of 0? Verified
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 ${{\log }_{b}}a$.
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.