Solve the equation. Write the solution set with the exact solutions. \[ \log _{3}(7 x-12)=\log _{3} x \] The solution set is $\square$.

Step 1 ：Set the arguments of the logarithms equal to each other: \(7x - 12 = x\)

Step 2 ：Subtract \(x\) from both sides to get: \(6x - 12 = 0\)

Step 3 ：Add 12 to both sides: \(6x = 12\)

Step 4 ：Divide both sides by 6 to solve for \(x\): \(x = 2\)

Step 5 ：Check if this solution is valid by substituting it back into the original equation: \(\log_3{(7*2 - 12)} = \log_3{2}\)

Step 6 ：Since both sides of the equation are equal, \(x = 2\) is a valid solution

Step 7 ：Therefore, the solution set is \(\boxed{\{2\}}\)