You can get logs using the following code:
Driver().Manage().Logs.GetLog();
You can specify what log you are interested in and then you can get the browser log, use the below code:
Driver().Manage().Logs.GetLog(LogType.Browser);
Also, don't forget to set up your driver accordingly:
ChromeOptions options = new ChromeOptions();
options.SetLoggingPreference(LogType.Browser, LogLevel.All);
driver = new ChromeDriver("path to driver", options);