In Apostol's book Introduction to Analytic Number Theory, we have the following exercise
4.18. Prove that the following two relations are equivalent: \begin{align*} \text{(a)} \quad \quad & \pi(x)=\frac{x}{\log x}+O \left( \frac{x}{\log^2 x} \right).\\ \text{(b)} \quad \quad & \vartheta(x)=x+O \left( \frac{x}{\log x} \right). \end{align*}
where $\pi(x)$ is, of course, the prime counting function, and $\vartheta(x)$ is Chebychev's function $\sum_{p \le x} \log p$.
I don't quite understand what "equivalent" is supposed to mean in this context, and I thought of skipping this particular exercise, but I suppose it would be a bad habit to skip all questions that I don't understand (especially since I am self-studying). So my hope is that someone would like to help me clarify this.