1. **State the problem:** Solve for $x$ in the equation $\log x + \log 12 = \log 8$. 2. **Recall the logarithm property:** $\log a + \log b = \log (a \times b)$. This means we can combine the left side. 3. **Combine the logs:** $$\log x + \log 12 = \log (12x)$$ So the equation becomes $$\log (12x) = \log 8$$ 4. **Since $\log A = \log B$, then $A = B$:** $$12x = 8$$ 5. **Solve for $x$: divide both sides by 12:** $$x = \frac{8}{12}$$ 6. **Simplify the fraction:** $$x = \frac{\cancel{8}}{\cancel{12}} = \frac{2}{3}$$ 7. **Final answer:** $$x = \frac{2}{3}$$