Answer
The error in the student’s solution occurs in the manipulation of the logarithmic expressions. Specifically, the incorrect assertion arises when simplifying the expression $ln(9) – ln(9)$ into $[1]$ instead of correctly noting it equals $0$. The mistake leads to $ln(x^2)=ln(3x)-[1]$, implying an incorrect deduction in solving for $x$. The correct approach should recognize that $ln(9)-ln(9)=0$, thereby maintaining the equality correctly.
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