${\mathrm{log}}_{2}n<n$

I know how to prove the base case Base Case ${\mathrm{log}}_{2}1<1$ likewise assuming the inequality for n=k; ${\mathrm{log}}_{2}k<k$

Then to prove by induction I show ${\mathrm{log}}_{2}k<(k+1)$?

I know it's true since the domain is all real numbers i just cant figure out the next step to prove it.