\[
5+\ln (x+1)=4
\]

Do not round any intermediate computations, and round your answ
\[
x=
\]

Step 1 ：Given the equation \(5 + \ln(x + 1) = 4\)

Step 2 ：Subtract 5 from both sides to get \(\ln(x + 1) = 4 - 5\)

Step 3 ：This simplifies to \(\ln(x + 1) = -1\)

Step 4 ：Exponentiate both sides of the equation to get rid of the natural logarithm, resulting in \(e^{\ln(x + 1)} = e^{-1}\)

Step 5 ：This simplifies to \(x + 1 = e^{-1}\)

Step 6 ：Subtract 1 from both sides to solve for x, resulting in \(x = e^{-1} - 1\)

Step 7 ：Substitute \(x = e^{-1} - 1\) back into the original equation to check the solution, resulting in \(5 + \ln((e^{-1} - 1) + 1) = 4\)

Step 8 ：Simplify the right side to get \(5 + \ln(e^{-1}) = 4\)

Step 9 ：Since \(\ln(e^{-1}) = -1\), the equation simplifies to \(5 - 1 = 4\)

Step 10 ：Therefore, the solution \(x = e^{-1} - 1\) is correct

Step 11 ：\(\boxed{x = e^{-1} - 1}\) is the final answer