That is definitely a perfectly good way of doing things. However, I like to encapsulate things. The client of that class hierarchy doesn't need to know what logger is being used, so allow for some default behavior. If the client wishes to override that behavior, then allow for a logger to be set, both in the constructor and by some 'setter'.

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We are the carpenters and bricklayers of the Information Age.

Don't go borrowing trouble. For programmers, this means Worry only about what you need to implement.