  In this paper, we investigate a nonlocal equation involving the logarithmic
Laplacian with indefinite nonlinearities: \begin{equation*} \left\{
\begin{array}{ll} L_\Delta u(x)=a(x_n)f(u), & x\in\Omega, \\ u(x)=0,& x\in
\mathbb{R}^n\backslash\Omega. \end{array} \right. \end{equation*} Here,
$\Omega$ represents a Lipschitz coercive epigraph. To achieve our objectives,
we develop a boundary estimate for antisymmetric functions, enabling us to
establish the monotonicity and nonexistence of bounded positive solutions for
the above problem using the direct method of moving planes.
