slothlife Posted August 22, 2016 Report Share Posted August 22, 2016 Hello! Can someone please confirm (or deny) if these two equations are equivalent? I'm unsure about my manipulation of the equation. I'm ultimately trying to obtain something that includes logs. Thanks in advance! ---> Reply Link to post Share on other sites More sharing options...
MikhailS Posted August 22, 2016 Report Share Posted August 22, 2016 You have expressed d in terms of f ie found inverse. These 2 expressions represent relations, in particular, functions. The domains and ranges of the two functions are not the same though. So, these are two different functions, but the relation they represent(think about it as a subset of cartesian product of two sets of real numbers) is essentially the same. Reply Link to post Share on other sites More sharing options...
kw0573 Posted August 23, 2016 Report Share Posted August 23, 2016 17 hours ago, MikhailS said: You have expressed d in terms of f ie found inverse. These 2 expressions represent relations, in particular, functions. The domains and ranges of the two functions are not the same though. So, these are two different functions, but the relation they represent(think about it as a subset of cartesian product of two sets of real numbers) is essentially the same. I think OP is taking this equation from physics or something, because of the "Hertz" and is more concerned if the equations are equivalent. I think the domain/ranges match if we take f to be positive real values and d be any real. f can only be positive because of the log function. Reply Link to post Share on other sites More sharing options...
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