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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?

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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.

This example simplifies the logarithmic expression 2 log 0.5 - log 225 + 2 log 0.3 + 6, using properties of logarithms such as the power rule and quotient rule. Step-by-step explanation suitable for students in Grades 10-12.

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