The given equation is:

$\log x = 1 + 3\log a - \log b$

Simplification Steps:

1. Apply the logarithmic property $\log a + \log b = \log (a \cdot b)$ and $\log a - \log b = \log \frac{a}{b}$.

$\log x = \log 10 + \log a^3 - \log b$

2. Combine terms into a single logarithmic expression:

$\log x = \log \left(\frac{10 \cdot a^3}{b}\right)$

3. Since the bases of the logarithms are equal, equate the arguments:

$x = \frac{10 \cdot a^3}{b}$

Final Result:

$x = \frac{10 \cdot a^3}{b}$

Would you like further explanations or help with related problems?

Follow-up Questions:

1. How do you simplify more complex logarithmic expressions?
2. What are the key properties of logarithms used in such problems?
3. How can logarithmic equations be solved when variables are exponents?
4. What are some practical applications of logarithms in real-world problems?
5. Can you derive this result without logarithmic properties (e.g., numerical substitution)?

Tip:

When solving logarithmic equations, always verify that the arguments of the logarithms remain positive to ensure validity.