How to formulate that an equation be shown to have no solutions? Is there any general way to formulate the statement that an equation has no solution?
For example:

Prove that this equation has no solution: $$x^{1/\log x}=5$$ 


N.B. Do not answer with a proof of the example.

Just say that $x$ doesn't exist:
$$
\nexists x \in \mathbb{C}\left[x^\left(1\over \log x\right) = 5\right]
$$
Slightly more formally:
$$
\forall x \left[x\in \mathbb{C} \implies x^\left(1\over \log x\right) \neq 5\right]
$$
