For #b>0#, #b!=1# and #y>0#, the symbol #x=log_{b}(y)# represents the unique real number such that #b^{x}=y# (it's the unique solution of that equation).

Since #x=3/2# is the unique solution of the equation #9^{x}=27#, it follows that #log_{9}(27)=3/2#.