To simplify the logarithmic expression \(\log\left(\frac{2}{3} \times 10\right)\), follow these steps:

1. Simplify the argument inside the logarithm:
   \[
   \frac{2}{3} \times 10 = \frac{20}{3}
   \]
   So, the expression becomes:
   \[
   \log\left(\frac{20}{3}\right)
   \]

2. Apply the logarithm property for division:
   \[
   \log\left(\frac{20}{3}\right) = \log(20) - \log(3)
   \]

Thus, the simplified form of \(\log\left(\frac{2}{3} \times 10\right)\) is:

\[
\log(20) - \log(3)
\]

If you'd like a numerical approximation, let me know!

Would you like to dive deeper into any part of this process?

Here are 5 related questions for practice:
1. Simplify \(\log(4 \times 5)\).
2. Solve \(\log\left(\frac{5}{6} \times 8\right)\).
3. How do you apply the logarithmic property for multiplication?
4. Simplify \(\log\left(\frac{1}{3} \times 9\right)\).
5. What is the logarithmic property for division?

**Tip**: When simplifying logarithmic expressions, remember that \(\log(a \times b) = \log(a) + \log(b)\) and \(\log\left(\frac{a}{b}\right) = \log(a) - \log(b)\).

Learn how to simplify the logarithmic expression Log(2/3 * 10). Follow step-by-step instructions to apply logarithmic properties, including multiplication and division rules. Suitable for students in Grades 9-11.

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