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The problem in the image asks to find the value of the following expression:

\[
\log_2 40 + \log_2 24 - \log_2 600 + \log_2 10
\]

We can simplify this using the properties of logarithms:

1. **Logarithm Addition**: \(\log_b(x) + \log_b(y) = \log_b(x \cdot y)\)
2. **Logarithm Subtraction**: \(\log_b(x) - \log_b(y) = \log_b\left(\frac{x}{y}\right)\)

### Step-by-step solution:

1. Combine the logarithms that are added:
   \[
   \log_2(40 \cdot 24) = \log_2(960)
   \]

2. Combine the subtraction:
   \[
   \log_2(960) - \log_2(600) = \log_2\left(\frac{960}{600}\right) = \log_2\left(\frac{8}{5}\right)
   \]

3. Lastly, add \(\log_2 10\):
   \[
   \log_2\left(\frac{8}{5}\right) + \log_2(10) = \log_2\left(\frac{8}{5} \cdot 10\right) = \log_2(16)
   \]

Since \(\log_2 16 = 4\), the final value is:

\[
4
\]

The value of the expression is **4**.

Would you like further details or clarifications? 

Here are five related questions for further practice:

1. What is the value of \(\log_2 32 - \log_2 8 + \log_2 4\)?
2. How do the properties of logarithms simplify expressions involving multiple logarithms?
3. What is the value of \(\log_3 81\)?
4. How do you convert logarithms with different bases?
5. How do logarithmic properties relate to exponential functions?

**Tip**: When working with logarithms, remember the properties of logarithms (product, quotient, and power rules) as they are useful in simplifying complex expressions.

Nilai dari ²log 40 + ²log 24 - ²log 600 + ²log 10 adalah . . .

Discover how to simplify the logarithmic expression ²log 40 + ²log 24 - ²log 600 + ²log 10 using logarithmic properties such as addition and subtraction rules. This step-by-step guide is perfect for students in Grades 10-12.

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