@Bohdan Kulish works fine and is cleaner but will delete the bottom part of the text. here is the code if you want to delete the top part

int lineCount = LogTextBox.LineCount;
        if (lineCount > 300)
        {
            string res = "";
            List<string> lines = new List<string>();

            for (int line = lineCount-1; line > 300; line--)
            {
                // GetLineText takes a zero-based line index.
                lines.Add(LogTextBox.GetLineText(line));
                res += LogTextBox.GetLineText(line) + "\n";
            }
            LogTextBox.Text = res;

        }