Let $X$ be a positive real number. Can someone help me by providing an asymptotic formula for this sum.

$$\sum_{n \leq X, n \equiv a \mod{b}} \log{n},$$

where $a$ and $b$ are two coprime integers. Thanks in advance.

Let $X$ be a positive real number. Can someone help me by providing an asymptotic formula for this sum.

$$\sum_{n \leq X, \; n\, \equiv\, a \mod{b}} \log{n},$$ where $a$ and $b$ are two coprime integers. Thanks in advance.