6e^3t=9e^2t

Answer 1

This is log work. Not certain what the problem is asking. As written, it is an identity.
6e^3t=9e^2t
e^18t=e^18t
which is hardly an issue.

Answer 2

huh? it's not (e^3t)^6 = (e^2t)^9

6e^3t = 9e^2t
e^t = 9/6
t = log 1.5