I'm not sure what you mean by avoid char by char comparative, but you at least need to read the common prefix from each of the strings, so the following algorithm is the best you can achieve (just iterate over the strings until they deviate or until the current longest prefix count is reached):
List<string> list = new List<string>()
{
"/home/texai/www/app/application/cron/logCron.log",
"/home/texai/www/app/application/jobs/logCron.log",
"/home/texai/www/app/var/log/application.log",
"/home/texai/www/app/public/imagick.log",
"/home/texai/www/app/public/status.log"
};
int maxPrefix = list[0].Length;
for(int i = 1; i < list.Count; i++)
{
int pos = 0;
for(; pos < maxPrefix && pos < list[i].Length && list[0][pos] == list[i][pos]; pos++);
maxPrefix = pos;
}
//this is the common prefix
string prefix = list[0].Substring(0, maxPrefix);