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 $e$.