On the number of solutions of some Kummer equations over finite fields

Let l be a prime number and let $k={\mathbb{F}}_q$ be a finite field of characteristic $p\ne l$ with $q=p^f$ elements. Let $n\ge 0$. We determine the number N of solutions $(x,y)$ in k of the Kummer equation$y^l=x(x^{l^n}-1),$ in terms of the trace of a certain Jacobi sum.