The expression \( 4 \log 3 + 4 \log 8 \) can be simplified using the logarithmic property:

\[
a \log b = \log b^a
\]

### Step 1: Apply the logarithmic property to both terms

\[
4 \log 3 = \log 3^4 = \log 81
\]
\[
4 \log 8 = \log 8^4 = \log 4096
\]

### Step 2: Add the logarithms

Using the property \( \log a + \log b = \log (a \cdot b) \), we can combine the two logarithms:

\[
\log 81 + \log 4096 = \log (81 \times 4096) = \log 331776
\]

Thus, the simplified expression is:

\[
\log 331776
\]

Would you like further details on logarithmic properties or how to solve different forms of logarithmic expressions?

Here are 5 related questions you can try:
1. Simplify \( 3 \log 5 + 2 \log 7 \).
2. Solve \( \log (2x) + \log (3y) = \log 18 \).
3. Simplify \( 2 \log 4 + 3 \log 6 \).
4. Solve \( \log 5x = 2 \).
5. Simplify \( \log a + \log b - \log c \).

**Tip:** Always look for opportunities to apply logarithmic properties like product, quotient, and power rules to simplify expressions.

This guide explains how to simplify the logarithmic expression 4log3 + 4log8 using the logarithmic power and addition rules. Learn how to combine terms step by step, applying the power rule to raise exponents and the addition rule to combine logarithms into a single logarithm. Suitable for students in Grades 9-12.

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