deletions | additions       diff --git a/untitled.tex b/untitled.tex  index 33fe111..da41d9d 100644  --- a/untitled.tex  +++ b/untitled.tex 
...
x=\mathrm{log}_{[b,b]}(a)=\mathrm{log}_b\left(\frac{a}{2}\right)\\  x=\mathrm{log}_{[b,b,b]}(a)=\mathrm{log}_b\left(\frac{a}{3}\right)\\  x=\mathrm{log}_{[b,b,b,b]}(a)=\mathrm{log}_b\left(\frac{a}{4}\right)\\  \end{equation}  Exploring more size $2$ sequences we have \begin{equation}  \mathrm{log}_{[1,3]}(10)=2\\  \mathrm{log}_{[1,3]}(11)=\frac{\ln 10}{\ln 3}\\  \mathrm{log}_{[1,3]}(12)=\frac{\ln 11}{\ln 3}\\  \mathrm{log}_{[1,3]}(28)=3\\  \end{equation}  giving generalised rule \begin{equation}  \ln3 \cdot \mathrm{log}_{[1,3]}(n)=\ln(n-1)  \end{equation}  and implying generalised rule \begin{equation}  \ln b \cdot \mathrm{log}_{[1,b]}(n)=\ln(n-1)  \end{equation}