Domain of f(x) = log |log x| is | vedclass

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Question

(C) The function $f(x) = \log |\log x|$ is defined if the argument of the logarithm is strictly positive.$1$. The inner logarithm $\log x$ is defined

Vedclass · Accepted Answer

$(0, 1) \cup (1, \infty)$

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(C) The function $f(x) = \log |\log x|$ is defined if the argument of the logarithm is strictly positive.$1$. The inner logarithm $\log x$ is defined only when $x > 0$.$2$. The outer logarithm $\log |\log x|$ is defined when $|\log x| > 0$.$3$. The condition $|\log x| > 0$ implies $\log x 
eq 0$,which means $x 
eq 1$.$4$. Combining both conditions,we require $x > 0$ and $x 
eq 1$.Therefore,the domain is $x \in (0, 1) \cup (1, \infty)$.

Domain of $f(x) = \log |\log x|$ is

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