Feng–Huang–Rao logarithmic commensurability conjecture for self-similar sets

Let $K,F$ be two totally disconnected, non-singleton self-similar sets in $\mathbb{R}^{n}$, which are the attractors of two iterated function systems with contraction-ratio sets $X,Y$, respectively. Suppose that there exists an affine map $f$ in $\mathbb{R}^{n}$ such that $f(F)\subset K$.

Logarithmic commensurability conjecture. The contraction ratios are logarithmically commensurable, meaning

$$Y\subset X^{\mathbb{Q}_{+}^{\ast}}.$$

This conjecture concerns the affine-embedding problem for totally disconnected self-similar sets and the inverse problem for generating iterated function systems. Its resolution is not established by the supplied text.