Define binary operations $♢$ and $♡$ by

$a♢b=a^{{\log }_7(b)}\text{and}a♡b=a^{\frac{1}{{\log }_7(b)}}$

for all real numbers $a$ and $b$ for which these expressions are defined. The sequence $(a_n)$ is defined recursively by $a_3=3♡3$ and

$a_n=(n♡(n-1))♢a_{n-1}$

for all integers $n\ge 4$. To the nearest integer, what is ${\log }_7(a_{2025})$?