In the study of the consequences of the prime number theorem, it is possible to find
an upper bound for $d(n)$, the number of divisors of a number $n$.
The example takes $n$ as the product of primes less than $x$ (I could not understand if it refers to the power one for a prime or greater).
Then it says that for the prime number theorem $$d(n) = 2^{\pi(x)} = 2^{{(1 + o(1)) \frac{x}{\log x}}}$$
Does someone understand the first passage?
Thanks.