Solve the equation. Write the solution set with the exact solutions. Also give approximate solution to 4 decimal plac
\[
\log (w-4)=3.5
\]
There is no solution, \{\}.
The exact solution set is
\[
w \approx \square
\]
Check
Answer
Final Answer: The exact solution set is \(\boxed{3166.2777}\)
Step 1 ：The given equation is in logarithmic form. To solve for w, we need to convert the equation into exponential form. The base of the logarithm is 10 (since it's not specified), so the equation becomes \(10^{3.5} = w - 4\).
Step 2 ：We can then solve for w by adding 4 to both sides of the equation, which gives us \(w = 10^{3.5} + 4\).
Step 3 ：Calculating the value of \(10^{3.5} + 4\) gives us \(w = 3166.2776601683795\).
Step 4 ：Rounding to 4 decimal places, we get \(w \approx 3166.2777\).
Step 5 ：Final Answer: The exact solution set is \(\boxed{3166.2777}\)
