Solve the logarithmic equation. Express all solutions in exact form. \[ \log (7-x)=0.5 \]

Step 1 ：The logarithmic equation is given as \(\log (7-x)=0.5\).

Step 2 ：The base of the logarithm in the given equation is not explicitly stated, which means it is 10 (common logarithm).

Step 3 ：The equation can be rewritten in exponential form as \(b^n = a\), or \(10^{0.5} = 7 - x\).

Step 4 ：Solving this equation will give the value of \(x\).

Step 5 ：\(10^{0.5} = 3.1622776601683795\)

Step 6 ：Substituting this value into the equation gives \(3.1622776601683795 = 7 - x\)

Step 7 ：Solving for \(x\) gives \(x = 3.8377223398316205\)

Step 8 ：Final Answer: The solution to the logarithmic equation \(\log (7-x)=0.5\) is \(\boxed{3.8377223398316205}\)