Log(5t)(5t + 1) * log(5x+1) (5t + 2) * log(5t+2 )(5t + 3)... log(5t+n)(5t +n +1)

I assume you're referring to the product,

Recall the change-of-base identity:

where c > 0 and c ≠ 1. This means the product is equivalent to

and it telescopes in the sense that the numerator and denominator of any two consecutive terms cancel with one another. The above then simplifies to

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