As I understand entryLog values you get from readLogFile(). So you can use java.util.Set to get list of unique IP addresses:
public int countDistinctClientIPAddresses() {
try {
readLogFile();
} catch (Exception e) {
// TODO Auto-generated catch block
e.printStackTrace();
}
Set<String> uniqueIPs = new HashSet<String>();
for (int k = 0; k < count; k++) {
uniqueIPs.add(entryLog[k].getCsIpAddress());
}
return uniqueIPs.size();
}