Domain of $f(x)=x^{\frac{1}{\log x}}$ What is the domain of $$f(x)=x^{\frac{1}{\log x}}$$
Since there is logarithm , the domain is $(0 \: \infty)$
But the book answer is $(0 \: \infty)-\{1\}$
but if $x=1$ $$f(x)=1^\infty=1$$
So is it necessary to exclude $1$

Just as MathematicsStudent1122 answered, if $$f=x^{\frac{1}{\log (x)}}$$ $$\log(f)=\frac{1}{\log(x)}\times\log(x)=1 \implies f=e$$ provided $x>0$.
