Question 131
It is known that $\{a_n\}$ is an arithmetic sequence with non-zero common difference and $\{b_n\}$ a geometric sequence, satisfying $a_1 = 3$, $b_1 = 1$, $a_2 = b_2$, $3a_5 = b_3$; furthermore, there are constants $\alpha$ and $\beta$ such that for every positive integer $n$, we have $a_n = \log_a b_n + \beta$. Then $\alpha + \beta = \underline{\hspace{2cm}}$.