Answer
417.9k+ views
Hint: First, we have to know that modulus is. After applying the condition, the value in the log cannot be less than 0. Since the value inside the modulus function returns a positive value. Then again apply the condition, the value in the log cannot be less than 0. Then, apply the condition for which the equation satisfies.
Complete step-by-step solution:
Given:- $f\left( x \right) = \log \left| {\log x} \right|$
Since \[\left| {\log x} \right|\] is in the log and we know that the value in the log cannot be less than 0. Then,
$ \Rightarrow \left| {\log x} \right| > 0$
A modulus function is a function that gives an absolute value to a number or variable. This results in the magnitude of the number of variables. It is often referred to as the function of absolute value. The output of the function is always positive irrespective of the data.
Since the value of $\log x$ can be either positive or negative. Then,
For the positive value of $\log x$, the value of $x$ will be,
$ \Rightarrow x \in \left[ {1,\infty } \right)$
For the negative value of $\log x$, the value of $x$ will be,
$ \Rightarrow x \in \left( {0,1} \right)$
Now, add both domains to get the actual domain of $x$,
$ \Rightarrow x \in \left( {0,1} \right) \cup \left[ {1,\infty } \right)$
Take the union of the domain on the right side,
$\therefore x \in \left( {0,\infty } \right)$
Thus, the domain of the function is $\left( {0,\infty } \right)$.
Hence, option (A) is the correct answer.
Note: The students might make mistakes in the log value as the log value can be less than 1 as the modulus function will give a positive value for the outer log.
Logarithms are the opposite of exponentials, just as the opposite of addition is subtraction and the opposite of multiplication is division.
In other words, a logarithm is essentially an exponent that is written in a particular manner.
Logarithms can make multiplication and division of large numbers easier, because adding logarithms is the same as multiplying, and subtracting logarithms is the same as dividing.
Complete step-by-step solution:
Given:- $f\left( x \right) = \log \left| {\log x} \right|$
Since \[\left| {\log x} \right|\] is in the log and we know that the value in the log cannot be less than 0. Then,
$ \Rightarrow \left| {\log x} \right| > 0$
A modulus function is a function that gives an absolute value to a number or variable. This results in the magnitude of the number of variables. It is often referred to as the function of absolute value. The output of the function is always positive irrespective of the data.
Since the value of $\log x$ can be either positive or negative. Then,
For the positive value of $\log x$, the value of $x$ will be,
$ \Rightarrow x \in \left[ {1,\infty } \right)$
For the negative value of $\log x$, the value of $x$ will be,
$ \Rightarrow x \in \left( {0,1} \right)$
Now, add both domains to get the actual domain of $x$,
$ \Rightarrow x \in \left( {0,1} \right) \cup \left[ {1,\infty } \right)$
Take the union of the domain on the right side,
$\therefore x \in \left( {0,\infty } \right)$
Thus, the domain of the function is $\left( {0,\infty } \right)$.
Hence, option (A) is the correct answer.
Note: The students might make mistakes in the log value as the log value can be less than 1 as the modulus function will give a positive value for the outer log.
Logarithms are the opposite of exponentials, just as the opposite of addition is subtraction and the opposite of multiplication is division.
In other words, a logarithm is essentially an exponent that is written in a particular manner.
Logarithms can make multiplication and division of large numbers easier, because adding logarithms is the same as multiplying, and subtracting logarithms is the same as dividing.
Recently Updated Pages
Mark and label the given geoinformation on the outline class 11 social science CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
When people say No pun intended what does that mea class 8 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Name the states which share their boundary with Indias class 9 social science CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Give an account of the Northern Plains of India class 9 social science CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Change the following sentences into negative and interrogative class 10 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Advantages and disadvantages of science
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Trending doubts
Bimbisara was the founder of dynasty A Nanda B Haryanka class 6 social science CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Which are the Top 10 Largest Countries of the World?
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
10 examples of evaporation in daily life with explanations
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Give 10 examples for herbs , shrubs , climbers , creepers
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
How do you graph the function fx 4x class 9 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Difference Between Plant Cell and Animal Cell
![arrow-right](/cdn/images/seo-templates/arrow-right.png)