if the products of the roots of the equation x²-3kx+2e^2logk-1=0 is 7, then the roots are real for k=..........

Product of the roots = 2e^{2 log k} – 1

⇒7= 2e^{2 log k} – 1

⇒2e^{2 log k} – 1 = 7

⇒2e^{2 log k} – 1 = 8

⇒e^{2 log k} = 4

⇒2log k = log 2²

⇒2log k = 2log 2

⇒k = 2