Solve the following for x. Round to the nearest tenth (1 decimal place). Answers will look like: 0.9 or 5.8

𝑙𝑛(𝑥+3)=4

To solve the equation \( \ln(x + 3) = 4 \), follow these steps:

### Step 1: Exponentiate both sides
To eliminate the natural logarithm (ln), exponentiate both sides of the equation using the base \( e \):
\[
e^{\ln(x + 3)} = e^4
\]
Since \( e^{\ln y} = y \), we get:
\[
x + 3 = e^4
\]

### Step 2: Calculate \( e^4 \)
Using the approximate value of \( e \approx 2.718 \):
\[
e^4 \approx 2.718^4 \approx 54.598
\]

### Step 3: Solve for \( x \)
Now, subtract 3 from both sides:
\[
x = 54.598 - 3
\]
\[
x \approx 51.6
\]

### Final Answer:
\[
x \approx 51.6
\]

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### Related Problems:
1. Solve \( \ln(x + 5) = 3 \) for \( x \).
2. Solve \( \ln(2x) = 4 \) for \( x \).
3. Solve \( \ln(x^2 + 4) = 5 \) for \( x \).
4. Solve \( e^{x+2} = 20 \) for \( x \).
5. Solve \( \ln(x - 7) = 6 \) for \( x \).

### Tip: 
Remember, to remove a natural logarithm, you exponentiate both sides using the base \( e \).

Solve the following for x. Round to the nearest tenth (1 decimal place). Answers will look like: 0.9 or 5.8

ln(x+3)=4

Learn how to solve the natural logarithm equation ln(x + 3) = 4 by exponentiating both sides. The detailed step-by-step solution covers logarithmic properties, exponentiation, and approximations of e. Suitable for students in Grades 9-12.

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