Let's analyze the given expression and simplify it step by step. The expression is:

$2 \log 0.5 - \log 225 + 2 \log 0.3 + 6$

Step 1: Simplify the logarithmic terms

1. For $2 \log 0.5$: Using the logarithmic property $a \log b = \log b^a$, we get: $2 \log 0.5 = \log (0.5^2) = \log 0.25$

2. For $- \log 225$: This term remains as it is for now: $- \log 225$.

3. For $2 \log 0.3$: Again, using the same property $2 \log 0.3 = \log (0.3^2) = \log 0.09$.

Step 2: Combine the logarithmic terms

Now we have: $\log 0.25 - \log 225 + \log 0.09 + 6$

Using the property $\log a - \log b = \log \left(\frac{a}{b}\right)$, we combine the logarithms: $\log \left(\frac{0.25 \times 0.09}{225}\right) + 6 = \log \left(\frac{0.0225}{225}\right) + 6$ Simplifying the fraction: $\log \left(1 \times 10^{-4}\right) + 6 = \log 10^{-4} + 6$

Step 3: Simplify the logarithm

$\log 10^{-4} = -4$

So, the expression becomes: $-4 + 6 = 2$

Thus, the answer is:

$\boxed{2}$

Would you like more details, or do you have any questions?

Here are 5 related questions to consider:

1. How do you apply logarithmic properties to simplify expressions?
2. What are the common logarithmic rules for multiplication and division?
3. Can you explain how $\log (a^b) = b \log a$ is used in problems?
4. What is the base of the logarithm assumed when it's written without a base (i.e., log)?
5. How does the logarithmic scale handle very small and very large numbers?

Tip: Always remember that logarithmic subtraction translates into division of arguments and multiplication applies for logarithmic addition.