When are “if” and “whether” equivalent?
Which one is the correct meaning of "Let me know if the problem persists."? Or is it ambiguous?
If the problem persists, let me know.
Let me know whether the problem persists or not.
tl;dr – ambiguous.
In informal writing, "if" and "whether" are used interchangeably.¹ This is not recommended because it creates ambiguity, but it is an unfortunate fact. Consequently, the statement can mean either:
A logician might say that the person being addressed need say anything only if the problem did persist. In practice, the context will usually make it clear what is required.