Confirmation about a equation (involves logs)

[slothlife]

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!

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[MikhailS]

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. 

[kw0573]

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.