4
log (base 2 sqrt 3) of 144 = log 144/log (2 sqrt 3) = log (12^2)/log(2 sqrt 3) 12 = 4*3 --> 12 = (2 sqrt 3)^2 => => log (12^2)/log(2 sqrt 3) = 2 log 12/log (2 sqrt 3) = 4 log (2 sqrt 3)/log(2 sqrt 3) = 4