You did not specified what kind of tool or programming language you want to use.
There are multiple tools to view log files. Just search the web for something like "log file viewer" or "log file analyzer".
Process the log file line by line. This can be done while reading line wise or by reading the whole content into an allocated buffer and operating on that. Both are common operations where many examples can be found in the web.
Write a function to get the timestamp from a line of the log file. How to do this depends on the format of the log file. If the log file contains ISO 8601 - Wikipedia
] datetimes, you can get it as string (ISO 8601 datetimes can be compared as strings to check for being before or after a specific datetime). Otherwise you have to convert them to a binary datetime format.
Then skip all lines that are before the start date. Display the lines until the end date is reached.