Solving a multi-step equation involving natural logarithms

Solve for $x$
\[
\ln (x+1)-\ln 4=-3
\]

Do not round any intermediate computations, and round your answer to the nearest hundred
\[
x=
\]

Step 1 ：The first step is to combine the logarithms on the left side of the equation using the properties of logarithms. The difference of two logarithms can be written as the logarithm of the quotient of the two numbers. So, the equation becomes: \(\ln \left(\frac{x+1}{4}\right) = -3\)

Step 2 ：Then, we can use the property of logarithms that says the logarithm of a number is equal to another number means that the base raised to the second number is equal to the first number. This gives us: \(\frac{x+1}{4} = e^{-3}\)

Step 3 ：Finally, we can solve this equation for x. x = 4*e^{-3} - 1

Step 4 ：The solution to the equation is \(x= \boxed{-0.80}\)