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The given expression is \( \log 4 - \log 5 \).

To combine these logarithms into a single logarithm, we can use the **logarithmic subtraction rule**, which states:

\[
\log_b A - \log_b B = \log_b \left(\frac{A}{B}\right)
\]

Here, \( A = 4 \) and \( B = 5 \). Applying the rule:

\[
\log 4 - \log 5 = \log \left(\frac{4}{5}\right)
\]

So, the simplified expression is:

\[
\log \left(\frac{4}{5}\right)
\]

Would you like any further details or explanations on this?

Here are 5 related questions to expand on this topic:
1. How can you simplify an expression like \( \log x - \log y + \log z \)?
2. What is the rule for combining logarithms with addition?
3. Can logarithmic expressions be simplified when different bases are involved?
4. How does the change of base formula for logarithms work?
5. What are the properties of logarithms when dealing with powers, such as \( \log_b(x^n) \)?

**Tip:** Always remember the basic logarithmic rules (product, quotient, and power) to simplify or combine logarithmic expressions efficiently.

Rewrite the logarithmic expression as a single logarithm with the same base. Simplify any fractions. log 4 - log 5

Learn how to simplify the logarithmic expression log 4 - log 5 by applying the logarithmic quotient rule. This step-by-step guide is perfect for high school students and covers key concepts in algebra and logarithms. Suitable for Grades 9-12.

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