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Stochastic resonance in Logistic model driven by time-modulated correlated multiplicative and additive noise is investigated. For small amount of the two noises, small amplitude of the additive modulated signal and small intensity of the time-modulated correlated noise, under the adiabatic approximation condition, the analysis expressions of the signal-to-noise ratios for different frequency and equal frequency of the two modulation forces have been obtained. Theoretical and numerical study shows that, the signal-to-noise ratios vary non-monotonously with the increase of the intensities of the multiplicative and additive noise. The curves of the signal-to-noise ratio versus additive noise strength present two peaks, while there is only one maximum value on each of the curve of the signal-to-noise ratio as a function of the multiplicative noise intensity. In addition, for equal frequency of the two modulation forces, the signal-to-noise ratio behaves non-monotonously with the increases of the amplitude of the time-modulation force.