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The derivation on the differential-valued field $\mathbb{T}_{\log}$ oflogarithmic transseries induces on its value group $\Gamma_{\log}$ a certainmap $\psi$. The structure $(\Gamma_{\log},\psi)$ is a divisible asymptoticcouple. We prove that the theory $T_{\log} = {\rm Th}(\Gamma_{\log},\psi)$admits elimination of quantifiers in a natural first-order language. All models$(\Gamma,\psi)$ of $T_{\log}$ have an important discrete subset$\Psi:=\psi(\Gamma\setminus\{0\})$. We give explicit descriptions of alldefinable functions on $\Psi$ and prove that $\Psi$ is stably embedded in$\Gamma$.

The Asymptotic Couple of the Field of Logarithmic Transseries