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Here is the equation I am talking about. I would like be sure that I know what everything stands for before I understand how it is formed.

[tex]T^{\frac{1}{2}}[/tex] is the Half-Life

[tex]ln(2)[/tex] I know this is a logarithm, but I am not sure why this is used in particular if anyone could explain why this is used I would be most grateful.

[tex]\lambda[/tex] is the Decay Constant

Here the equation is.

[tex]T^{\frac{1}{2}} = \frac{ln(2)}{\lambda}[/tex]

Any help on how this equation is constructed would be great, It would be nice to see a step by step method in how you would get there. I'm not sure if there is really much to say on the construction, but even an explantion on how it is constructed would be nice.