The error happens in the last line.
The relevant log rule is ln(A) - ln(B) = ln(A/B)
The issue is that the 0 isn't ln(0), so that 0 cannot be thrown into the natural log like that.
What we can do is this set of steps
ln(3x) - 0
ln(3x) - ln(1)
ln(3x/1) ... applying the log rule mentioned
ln(3x)
But these steps are a needlessly overcomplicating things. We can simply go from ln(3x)-0 to ln(3x) in one step. Subtracting off zero doesn't change ln(3x) at all.
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Let's continue the steps to solve for x.
ln(x^2) = ln(3x)
x^2 = 3x
x^2-3x = 0
x(x-3) = 0
x = 0 or x-3 = 0
x = 0 or x = 3
Those are the two possible solutions.
However, x = 0 isn't valid because it's not in the domain of ln(x^2). In other words, ln(0) isn't defined. The domain of y = ln(x) is x > 0
This means that x = 3 is the only solution.