From Förberedande kurs i matematik 1

By writing the argument \displaystyle \text{8} as \displaystyle 8=2\centerdot 4=2\centerdot 2\centerdot 2=2^{3}, the logarithm law, \displaystyle \lg a^{b}=b\lg a, gives

\displaystyle \log _{2}8=\log _{2}2^{3}=3\centerdot \log _{2}2=3\centerdot 1=3

where we have used \displaystyle \log _{2}2=1.