Applying the x = e^t substitution

Thanks 'topsquark' for the suggestion to substitute e^t for x in my partial working. Here's my attempt at the rest of the problem - I get a very neat result which makes me think perhaps it is correct. Here's the rest from where I got stuck:

lnp = lne^(-6) * lnx + lnK

(lnp - lnK)/(lne^(-6)) = lnx = lne^t = t (if x = e^t)

t = (ln(p/K))/ (lne^6) = (ln(p/K))/6

6t =ln(p/K)

e^(6t) = p/ K

p = Ke^(6t) = K(e^t)^6 = Kx^6

p = Kx^6 (K is a constant)

Could someone venture a verdict please??(Wondering)