Solve the following equation. \[ \log _{2}(6 x+3)=2 \] The solution set is

Step 1 ：The given equation is \(\log _{2}(6 x+3)=2\).

Step 2 ：To solve for x, we need to convert the logarithmic equation into an exponential equation. The base of the logarithm becomes the base of the power, the right side of the equation becomes the exponent, and the argument of the logarithm becomes the result.

Step 3 ：This gives us the equation \(2^2 = 6x + 3\).

Step 4 ：Solving for x, we get \(x = \frac{1}{6}\).

Step 5 ：Final Answer: The solution set is \(\boxed{\frac{1}{6}}\).