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Half Life Formula :

$$\text{N}\left(t \right)\;=\;\text{N}_0\;*\;\left(\frac{1}{2}\right)^\frac{t}{t_\frac{1}{2}}$$

Where,

N(t) =quantity of the substance remaining

N0 =initial quantity of the substance

t =time elapsed

t1/2 =half life of the substance

Now, we have the formula for the half-life of a substance.

$$\text{N}\left(t \right)\;=\;\text{N}_0\;*\;\left(\frac{1}{2}\right)^\frac{t}{t_\frac{1}{2}}$$

$$\frac{\text{N}\left(t \right)}{\text{N}_0}\;=\;\left(\frac{1}{2}\right)^\frac{t}{t_\frac{1}{2}}$$

$$\text{Log}_\frac{1}{2}\left(\frac{\text{N}\left(t \right)}{\text{N}_0}\right)\;=\;\left(\frac{1}{2}\right)^\frac{t}{t_\frac{1}{2}}$$

$$\text{t}_\frac{1}{2}\;=\;\frac{t}{\text{Log}_\frac{1}{2}\left(\frac{\text{N}\left(t \right)}{\text{N}_0}\right)}$$