<p>This paper investigates the well-posedness, global existence and stability of a logarithmic nonlinear plate equation incorporating strong damping and a fractional time-delay term represented by the tempered Caputo derivative. To the best of our knowledge, this is the first study in which the tempered Caputo derivative acts directly on the delayed term within a plate equation. The local existence and uniqueness of weak solutions are established using semigroup theory, and global existence is derived through energy estimates. Exponential stability is proved by constructing an appropriate Lyapunov functional, and the analytical results are further supported by numerical simulations that demonstrate exponential energy decay. The analysis highlights the significant influence of the fractional time-delay and damping effects on the long-term stability of the system.</p>