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