To solve the equation \( 2 \log 8 = 3 \), let's break it down step-by-step:

1. Divide both sides by 2 to isolate the logarithmic term:
   \[
   \log 8 = \frac{3}{2}
   \]

2. This equation means: \(\log_{10} 8 = \frac{3}{2}\), assuming it's a common logarithm (base 10).

3. Now, recall that \(\log_{10} 8 = x\) implies \(10^x = 8\).

   So, \( 10^{\frac{3}{2}} = 8 \).

4. Simplify \( 10^{\frac{3}{2}} \):
   \[
   10^{\frac{3}{2}} = \sqrt{10^3} = \sqrt{1000}
   \]

   This gives approximately \( \sqrt{1000} = 31.62 \).

5. Therefore, \( 31.62 \approx 8 \) is false.

Hence, the equation is only valid if it's interpreted in a different logarithmic base, specifically base 2.

Would you like more details, or do you have questions? Here are some related questions for practice:

1. What is the value of \(\log_2 8\)?
2. How do you convert logarithms of different bases?
3. What does \(\log_{10} 1000\) equal?
4. Solve \(3 \log 5 = 6\) for \(\log 5\).
5. What is the general form of a logarithmic equation?

**Tip:** When working with logarithms, always verify the base being used (common or natural logarithm).

Explore how to solve the logarithmic equation ²log 8 = 3, involving logarithms, their properties, and the importance of specifying the base. This solution covers core logarithmic concepts and provides detailed steps. Suitable for students in Grades 9-11.

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