Solve for $x$ \[ \log _{2}(x+6)=\log _{2}(x+3)+2 \] If there is more than one solution, separate them with commas. If there is no solution, click on "No solution". \[ x= \]

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

Step 2 ：Since the equation involves logarithms with the same base, we can use the property of logarithms that states if \(\log_b{a} = \log_b{c}\), then \(a = c\). Therefore, we can set the arguments of the logarithms equal to each other and solve for \(x\).

Step 3 ：However, when we do this, we get \(x = x\), which is not a valid equation.

Step 4 ：This means that the solution set is empty, and there is no real number solution for the equation.

Step 5 ：Final Answer: \(\boxed{\text{No solution}}\)