Explanation:
Let's use the log rules:
When we have the difference of 2 logs with the same base, it's like having a log with the same base as the base of our 2 logs, but the argument will be the quotient between the 2 arguments:
log(3u) + log(u-2) = 0
log[(3u)/(u-2)] = 0
By definition of log:
(3u)/(u-2) = 1
u ≠2
3u = u - 2
4 u = -2
u = -1/2
This should be the result.
I forgot the initial existance conditions:
u > 2.
Means that there is no solution to this equation.