Solve for t:
6^(3 t - 1) = 36^(t - 3)
Take the natural logarithm of both sides and use the identity log(a^b) = b log(a):
log(6) (3 t - 1) = log(36) (t - 3)
Expand out terms of the left hand side:
3 log(6) t - log(6) = log(36) (t - 3)
Expand out terms of the right hand side:
3 log(6) t - log(6) = log(36) t - 3 log(36)
Subtract t log(36) - log(6) from both sides:
(3 log(6) - log(36)) t = log(6) - 3 log(36)
Divide both sides by 3 log(6) - log(36):
t = (log(6) - 3 log(36))/(3 log(6) - log(36)) = - 5