A = k - p·ln(x)

Solve for ln(x)

add p·ln(x) to both sides:

p·ln(x) + A = k

Subtract A from both sides:

p·ln(x) = k - A

Divide both sides by p

        k - A 
ln(x) = —————
          p

Now you need to know this principle:  

The natural log equation  is equivalent to the 
exponential form,  

So the above becomes:

 x = e

Edwin