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We connect two developments that aim to extend Voevodsky's theory of motives over a field in such a way as to encompass non-
$\mathbf {A}^1$-invariant phenomena. One is theory of reciprocity sheaves introduced by Kahn, Saito and Yamazaki. The other is theory of the triangulated category 
$\operatorname {\mathbf {logDM}}^{{\operatorname {eff}}}$ of logarithmic motives launched by Binda, Park and Østvær. We prove that the Nisnevich cohomology of reciprocity sheaves is representable in 
$\operatorname {\mathbf {logDM}}^{{\operatorname {eff}}}$.
