x = xo + vo t + (1/2) a t2 where x is the displacement at time t,
xo is the displacement at time t = 0, 
vo is the velocity at time t = 0, 
a is the constant acceleration
Dimensionally correct. Each term has dimensions of L.
P =  where P is pressure,
r is density, 
g is gravitational acceleration, 
h is height
Not dimensionally correct.
[P] = M·L-1·T-2
[] = M1/2·L-1/2·T-1
ln Nd/Na = - [ Vghd(r - rl)] / kT where Nd and Na are number of 
particles, V is volume, 
g is gravitational acceleration, 
hd is distance, 
r and rl are densitites, 
k is Boltzmann's constant with SI units of joules per kelvin, 
T is absolute temperature.
Dimensionally correct.  Left side of the equation is "dimensionless".
[Vghd(r-rl)] = M·L2/T2.
kT has SI units of joules, (which is a unit  of energy), and therefore [kT] = M·L2/T2.
Right side of the equation is also "dimensionless", 
since (M·L2/T2)/(M·L2/T2) =1.

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