A student is trying to solve the equation

Here is the student's working:

$$\begin{array}{rl}2\times 3^{2x+1}& =10\\ \log (2\times 3^{2x+1})& =\log (10)\\ (2x+1)\log (2\times 3)& =1\\ 2x+1& =\frac{1}{\log (6)}\\ x& =\frac{1}{2}(\frac{1}{\log (6)}-1)\end{array}$$

1. Explain the student's mistake.

2. Give the correct answer to $3$ significant figures.

The error occurs going from line 2 to line 3 in the working.