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\mathrm{log}_{[1,2]}(10)=\frac{2\ln3}{\ln2}\\  \mathrm{log}_{[1,2]}(17)=4\\  \end{equation}  Which actually corresponds to a general rule \begin{equation}  \ln2 \mathrm{log}_{[1,2]}(n)=\ln(n-1)  \end{equation}  We then not that if a number is repeated we have \begin{equation}  x=\mathrm{log}_{[b,b]}(a)=\mathrm{log}_b\left(\frac{a}{2}\right)\\