Solve the exponential equation. Write the exact answer with natural logarithms and then approximate the result.
\[
e^{x+4}=7
\]
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A. The exact answer(s) with natural logarithms is/are $x=$ (Use integers or fractions for any numbers in the expression. Use a comma to separate answers as needed.)
B. There is no solution. The solution set is the empty set, $\varnothing$.
Answer
\(\boxed{x \approx -2.05}\) is the approximate result
Step 1 ：Given the exponential equation \(e^{x+4}=7\)
Step 2 ：Take the natural logarithm (ln) on both sides of the equation to get \(x+4 = \ln(7)\)
Step 3 ：Subtract 4 from both sides of the equation to isolate 'x', so \(x = \ln(7) - 4\)
Step 4 ：Approximate the result to get \(x \approx -2.05\)
Step 5 ：\(\boxed{x = \ln(7) - 4}\) is the exact answer with natural logarithms
Step 6 ：\(\boxed{x \approx -2.05}\) is the approximate result
