The expression \((7/8) \log_2(8/7)\) can be simplified as follows:

\[
\text{Expression: } \frac{7}{8} \log_2 \left(\frac{8}{7}\right)
\]

This expression is a product of a fraction \(\frac{7}{8}\) and the logarithm \(\log_2\left(\frac{8}{7}\right)\). Since this logarithm represents the power to which the base 2 must be raised to obtain the value \(\frac{8}{7}\), the expression itself cannot be simplified much further without numerical evaluation.

Would you like to evaluate it numerically or keep it in this form?

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Would you like details or have any questions? Here are 8 related questions for further exploration:

1. What is the approximate value of \(\log_2(8/7)\)?
2. How does changing the base of the logarithm affect the expression?
3. What is the significance of the base in logarithmic expressions?
4. How can this expression be represented using natural logarithms?
5. What happens if the fraction \(\frac{7}{8}\) is modified?
6. Can you express this logarithm in terms of the difference of two logarithms?
7. How would this expression change if the fraction was flipped to \(\frac{8}{7}\)?
8. What are some real-world applications of logarithmic expressions like this one?

**Tip:** When simplifying logarithmic expressions, consider whether the logarithm can be broken down or if the base can be changed for easier computation.

Explore how to simplify the mathematical expression (7/8)log2(8/7) step-by-step. Understand the relationship between fractions and logarithms, and learn about the significance of logarithmic bases. Suitable for advanced high school students and beyond.

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