Schneider–Lang–Ramachandra's exponential conjecture

Let $M$ be a $2\times2$ matrix whose entries are logarithms of algebraic numbers. Assume that the rows of $M$ are linearly independent over ${\mathbb Q}$ and that its columns are linearly independent over ${\mathbb Q}$.

Schneider–Lang–Ramachandra's exponential conjecture. Under these assumptions, the determinant of $M$ is nonzero.

The source invokes this conjecture to derive the cubic totally real norm-one torus case of the torus analogue of Mazur's conjecture. It is presented as a well-known conjecture in transcendental number theory and is not established in the paper.