Put into Cartesian form with x>0

$\displaystyle x=5e^t$ $\displaystyle y=3e^{-t}$

I solved for t:

$\displaystyle t=ln_e(x/5)$

Found the Cartesian:

$\displaystyle y=3e^{-ln_e(x/5)}$

This is how I got the final answer of 15/x and I'd like to know if, mathematically, I'm allowed to do it this way(I might leave out some steps, but I think you will understand. Let me know if you want me to add those steps):

$\displaystyle y=3/e^{ln(x/5)}$

Multiply both sides by $\displaystyle e^{ln(x/5)}$

Change to the form:$\displaystyle yln_e(x/5) = ln_e3$

Divide both sides by $\displaystyle ln_e$

(yx)/5 = 3

Multiply both sides by 5, then divide both sides by x.

Final answer 15/x

The correct answer is 15/x

Sorry about not using MATH tags all the way through. I'm under time constraints and am not very familiar/savvy with MATH tags.