What is the domain of the function \(f(x)=\log_{x}e\)?
\((0,\infty)-\{1\}\)
\(f(x)=\log_{x}e=\dfrac{1}{\ln x}\) requires the base \(x>0\) and \(x\neq 1\) (since \(\ln x=0\) there, making the expression undefined). Hence the domain is \((0,\infty)-\{1\}\).
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