Question: User: $\log\left(x+3\right)=2+\log^2$
1. **State the problem:** Solve the equation $$\log(x+3) = 2 + \log^2$$ for $x$.
2. **Analyze the equation:** The equation as given is ambiguous because $\log^2$ is not a standard notation. It could mean $(\log)^2$ or $\log(2)$. Assuming the user meant $\log^2$ as $\log(2)$, the equation becomes:
$$\log(x+3) = 2 + \log(2)$$
3. **Recall logarithm properties:**
- $\log(a) + \log(b) = \log(ab)$
- $\log(a^b) = b\log(a)$
4. **Rewrite the right side:**
$$2 + \log(2) = \log(10^2) + \log(2) = \log(100) + \log(2) = \log(100 \times 2) = \log(200)$$
5. **Set the equation:**
$$\log(x+3) = \log(200)$$
6. **Since logarithm is one-to-one:**
$$x + 3 = 200$$
7. **Solve for $x$:**
$$x = 200 - 3 = 197$$
**Final answer:**
$$x = 197$$