BPP(complexity) with binary form of number

Question

For any language $L \subseteq \mathbb{B^{*}}$ we define language $L^{log}$ as set $\{\overline{a}\overline{b} | \overline{a} \in L, \, \overline{b} - \text{binary form of number}\,\, |\overline{a}|\}.$

Prove:

if $L \in \mathbf{BPP}$, then $L^{log} \in \mathbf{BPP}$.

Any hint how to start it?