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

The solution set is $\square$.

Answer

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Answer

Therefore, the solution set is $\boxed{\{2\}}$

Steps

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 $\boxed{\{2\}}$