[Math] On the sum of the logarithms of primes.

Question

Let $p$ be a prime and $x$ be an integer. It is known that $\sum_{p\leq x} \log p = O(x)$, and i think this is equivalent to the Prime Number Theorem.
As a mere prospective undergraduate with only a minimal understanding of analytic number theory, i'm curiously wondering if there exists an analogous formula for $\sum_{p\leq x} \log(p-1)$ ?

Answer 1

$$\log(p-1)=\log(p)+\log(1-\frac1p)\approx\log(p)-\frac1p$$

https://en.wikipedia.org/wiki/Divergence_of_the_sum_of_the_reciprocals_of_the_primes