Question

How do I find the domain of $\ln \left( {x - 1} \right)$?

Answer 1

Hint: To solve such questions always remember that the domain of a function is the set of all possible values of the independent variables. If a certain value does not satisfy the given function, then those values will not be included in the domain. Also, the natural log should always be greater than zero.

Complete step-by-step solution:
Given the function $\ln \left( {x - 1} \right)$.
Here it is asked to find the domain of the given function.
It is known that in the case of logarithms the domain should always be positive.
Therefore, in the given function $\ln \left( {x - 1} \right)$, it can be seen that,
$x - 1 > 0$
Or it can be written as,
$x > 1$
This is the domain of the given function.

Therefore, the interval notation of the domain of the given function $\ln \left( {x - 1} \right)$ is $\left( {1,\infty } \right)$.

Additional Information: A relation F is said to be a function if each element in set A is associated with exactly one element in set B. $\ln \left( x \right)$ can also be written as ${\log _e}\left( x \right)$. Here $e$ is known as the base of the log. To represent the domain and range of a function one can use interval notation or can also use inequalities.

Note: To solve such questions remember that domain is the set of all possible values of a function and range is the set of all possible output of the function. To compute the domain and the range of a given function, first, we have found all the possible values that satisfy the given function and then find the output of the function based on these values.