I guess when you say you want a cartesian equation of the curve, you would have to express them in cartesian coordinates of x and y. Thus, you must get rid of the variable t. The solution is as follows:
x = t⁴ y = ln(t)
e^y = e^(lnt) e^y = t
Substuting this to the first equation, x = (e^y)⁴ <em>x = e^4y</em>
