A simultaneous approximation problem for exponentials and logarithms

Veekesh Kumar, Riccardo Tosi

Let ${\alpha }_1,{\alpha }_2$ be non-zero algebraic numbers such that $\frac{\log {\alpha }_2}{\log {\alpha }_1}\notin \mathbb{Q}$ and let $\beta$ be a quadratic irrational number. In this article, we prove that the va…