Question
Find the value of $x$ which satisfies the following equation.
\[
\ln (-7 x-4)=3
\]
Round your final answer to 4 decimal places, and do not include " $x=$ " in your answer.
Provide your answer below:
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Answer
Rounding to 4 decimal places, we get the final answer: \(\boxed{-3.4408}\).
Step 1 ：The given equation is in the form of a natural logarithm. To solve for x, we need to convert the equation from logarithmic form to exponential form. The base of natural logarithm is 'e'. So, the equation can be rewritten as \(e^3 = -7x - 4\).
Step 2 ：Then, we can solve for x: \(x = \frac{e^3 + 4}{-7}\).
Step 3 ：Calculating the above expression, we get \(x = -3.4407909890268096\).
Step 4 ：Rounding to 4 decimal places, we get the final answer: \(\boxed{-3.4408}\).
