In this study, we consider a variant of a generalized Laplace transform represented by a logarithmic function. The tool of the proposed research is the substitution to logarithmic function. In addition, we investigated the existence and uniqueness theorem on the variant of Laplace transform. The obtained result has a strong point in existence theorem because of its simplicity. As a result, the proposed theorem does not need the exponential function in the condition of growth restriction. The main objective of this paper is to apply the result in a new generalized integral transform.

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