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We consider in this paper a large class of perturbed semilinear wave equationwith subconformal power nonlinearity. In particular, we allow log perturbationsof the main source. We derive a Lyapunov functional in similarity variables anduse it to derive the blow-up rate. Throughout this work, we use some techniquesdeveloped for the unperturbed case studied by Merle and Zaag [12] together withideas introduced by Hamza and Zaag in [5] for a class of weather perturbations.

The blow-up rate for strongly perturbed semilinear wave equations