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Align :=, =, and =: symbols

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What is the best way to get the symbols \coloneq, =, and \eqcolon (provided by package mathtools) to align in a nice way (so the equals part of each is aligned) in an align environment?

I can get the first two to align nicely by putting the & afterward and using an empty field to get the mathrel alignment right, as follows, ...but the third is badly aligned.

r(x) \coloneq{}& \log x^{-(k+1)} + k\\            ={}& -\log x \quad\text{if } k=0\\     \eqcolon{}& s(x)

enter image description here

Likewise, if I left-align them, the second two are well-aligned, but the firstone isn't:

r(x) &\coloneq \log x^{-(k+1)} + k\\&= -\log x \quad\text{if } k=0\\&\eqcolon s(x)

enter image description here

I suppose I could nudge things around with some ad hoc adjustments, but, is there a better way fix this?


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