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