1. **State the problem:** Solve the equation $3\log(x+4) = 6$ for $x$. 2. **Recall the logarithm property:** If $a\log_b(c) = d$, then $\log_b(c) = \frac{d}{a}$. 3. **Apply the property:** $$3\log(x+4) = 6 \implies \log(x+4) = \frac{6}{3} = 2$$ 4. **Rewrite the logarithmic equation in exponential form:** $$\log(x+4) = 2 \implies 10^2 = x+4$$ 5. **Calculate the power:** $$100 = x + 4$$ 6. **Solve for $x$:** $$x = 100 - 4 = 96$$ 7. **Check the domain:** Since $x+4 > 0$, $x > -4$. Our solution $x=96$ satisfies this. **Final answer:** $$x = 96$$