This was a fun problem. Here's my answer. For the function we write the equation of the tangent line to the point as Similarly, for the function we write the equation of the tangent line as Now, given that and we can immediately write down the equations of the tangent lines:

and

We want to set these equal. Obviously, this will have to happen when so re-define and set

Solving for yields

Plugging this back into either or (it shouldn't matter, although I did it in both as a check, and they both come out the same), you get

This is valid when