C# :: Static Class For Logging?

I am developing logging class and it loos like below now, my question here is I would like to avoid situation to call this class methods multiple times in same time - as I've read when I have static class or even static method (not exactly whole class) it can be call only once in time. Is this true and whether my class would pass the concept to avoid multi accessing - lets say in case of multithreading case - if one task would try to call statuc method when there is already some other trad using it.

public static class Log {
public static string EngineName { get; set; }
private static List<String> logdata = new List<string>();
public static void LogMessage(string msg, ELogflag flag, string title = "") {
StringBuilder sb = new StringBuilder();

[code]....

And my new Enum:

enum ELogflag {
LOG,
ENGINE,
CRITICAL,
CUSTOM
}