To expand the logarithmic expression using the properties of logarithms, let’s review the expression.

Please share the specific expression you'd like expanded, and I’ll apply the logarithmic properties, such as:

1. Product Rule: $\log_b (MN) = \log_b M + \log_b N$
2. Quotient Rule: $\log_b \left(\frac{M}{N}\right) = \log_b M - \log_b N$
3. Power Rule: $\log_b (M^p) = p \cdot \log_b M$

Once you provide the expression, I can expand it in detail for you.

Would you like to upload an image, or type out the expression?

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Here are five relevant questions to deepen your understanding of logarithmic expansions:

1. How does the power rule apply to expressions with fractional exponents?
2. What happens when expanding a logarithmic expression with multiple products and quotients?
3. Can you apply the expansion rules when the logarithmic base is different, such as natural logarithms?
4. How do you handle nested logarithmic functions during expansion?
5. When might you use a change of base formula in logarithmic expansions?

Tip: Always simplify inside the logarithm as much as possible before applying expansion properties for cleaner results!