For example . A more interesting example is given by and .

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- May 26th 2011, 05:18 AM #1

- May 26th 2011, 05:26 AM #2

- May 26th 2011, 05:59 AM #3

- May 27th 2011, 08:45 AM #4
This is how I might attempt to do this problem. I will assume that both and are smooth. Taking the natural log of both sides gives

.

Call the term on the RHS . Differentiating both side wrt and gives

.

Thus, where and are constant.

So

so .

Now set and this gets you the form for Then substitute into the original functional equation to determine .

- May 29th 2011, 03:05 PM #5