Expressing the derivative of the exponential function, as $\log(x)$.

What is the best way to say that a function can be expressed as $\log(x)$?
My thoughts are:

The derivative of the function
$f(x) = e^{x}$ equals the function
$\log(x)$.

Is that correct?

A:

Something that will be much more correct is to say that the derivative of $e^{x}$ is $\log{x}$.
Another thing that is better than “The derivative of the function $f(x) = e^x$ equals the function $\log(x)$” is to say that the derivative of $f(x)$ is $\frac{f'(x)}{f(x)} = \frac{d}{dx} e^{x} = \log{x}$. (This latter thing would be a good thing to say even if it didn’t turn out to be true; it’s just that the second sentence is more likely to be true than the first.)

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