How can I express this function in terms of s and t?

Question

I suppose that this equality can be satisfied: $$ \frac{t}{x^s}=\frac{1}{x^{Y(s,t)}} $$

Where $ Y(s,t) $ is a function of s and t.

Is there a function sloution for $Y(s,t)$?

Answer 1

hint

$${x^{Y(s,t)}}=e^{lnx Y(s,t)}$$