We have that after 1 half-life, the reactant reaches half its concentration 
. After 2 half-lives it reaches 
of its concentration, namely one-fourth. After n half lives we have that it reaches 
of its initial concentration. Thus, we have to solve the equation 
. Taking the log base 2 of each part of the equation we get from logarithm properties: ![log_{2}[(1/2)^n]=log_{2}(2^{-n})=-n](https://tex.z-dn.net/?f=log_%7B2%7D%5B%281%2F2%29%5En%5D%3Dlog_%7B2%7D%282%5E%7B-n%7D%29%3D-n)
. The other hand yields: 
. Solving for n we get that n=1.74. Thus, after around 1.74 half lives the concentration becomes 30% of the initial one. Note how this is consistent with our previous analysis; if we let it a little bit more, 2 half-lives, the concentration will become 25% of the initial.