To solve the expression \( \log_2 64 + \log_3 27 + \log_5 125 \), we will evaluate each logarithm individually and then sum them up.

### Step 1: Evaluate \( \log_2 64 \)
The logarithm \( \log_2 64 \) asks the question: "To what power must 2 be raised to get 64?"

Since \( 64 = 2^6 \), we have:
\[
\log_2 64 = 6
\]

### Step 2: Evaluate \( \log_3 27 \)
The logarithm \( \log_3 27 \) asks the question: "To what power must 3 be raised to get 27?"

Since \( 27 = 3^3 \), we have:
\[
\log_3 27 = 3
\]

### Step 3: Evaluate \( \log_5 125 \)
The logarithm \( \log_5 125 \) asks the question: "To what power must 5 be raised to get 125?"

Since \( 125 = 5^3 \), we have:
\[
\log_5 125 = 3
\]

### Step 4: Add the results
Now, sum the results from the previous steps:
\[
\log_2 64 + \log_3 27 + \log_5 125 = 6 + 3 + 3 = 12
\]

So, the final answer is:
\[
\boxed{12}
\]

Would you like more details or have any questions? Here are some related questions you might find interesting:

1. How do you evaluate logarithms with different bases?
2. What is the general process to solve a logarithmic equation?
3. Can you solve \( \log_2 32 + \log_4 16 \)?
4. How would you simplify \( \log_2 64 \times \log_3 27 \times \log_5 125 \)?
5. What is the relationship between logarithms and exponents?
6. How can you use the change of base formula to evaluate logarithms?
7. Can you explain the concept of logarithmic scales?
8. What is the importance of logarithms in real-world applications?

**Tip:** When working with logarithms, it's helpful to recognize common powers of small numbers like 2, 3, 5, etc., to quickly evaluate logarithms without a calculator.

Learn how to evaluate logarithms with different bases: log2 64, log3 27, and log5 125. Understand the properties of logarithms and apply the logarithm addition property to solve this mathematical expression. Suitable for Grades 9-12.

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