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\log_{[\zeta(1)]}(\zeta(3))=3\\  \end{equation}  Then we see that (at least for the basic support) \begin{equation}  \log_{[\zeta(1)]}(\zeta(s))=s \log_{[\zeta(1)]}(\zeta(s))=s\\  \mathrm{inv}[\zeta(s)]=\log_{[\zeta(1)]}(s)  \end{equation} the log is then the inverse function!