https://file.aiquickdraw.com/mathbot/file/1726241278724pdorhr3t.jpg

The given expression from the image is:

\[
\left(5 - \log_2 13\right) \left(\log_{32/13} 95 + \log_{13/32} 47.5\right)
\]

### Step-by-step simplification:

1. **Simplifying the first part**:
   \[
   5 - \log_2 13
   \]

2. **Simplifying the second part**:
   \[
   \log_{32/13} 95 + \log_{13/32} 47.5
   \]

Let's approach this step by step and handle the logarithmic terms, applying logarithmic properties and simplifying numerically where necessary. I will now calculate the exact result for you.The result of the expression

\[
\left(5 - \log_2 13\right) \left(\log_{32/13} 95 + \log_{13/32} 47.5\right)
\]

is approximately 1.

Would you like further details or any clarifications?

Here are some related questions you might find useful:
1. How do you change the base of a logarithm?
2. What are the common logarithmic properties that simplify such expressions?
3. How is the natural logarithm different from base-2 logarithms?
4. Can you explain how to solve logarithmic equations algebraically?
5. What real-world problems can be modeled using logarithmic functions?

**Tip**: Logarithms are often used in solving exponential growth and decay problems, so mastering their properties is crucial!

(5 - log_2 13)(log_(32/13) 95 + log_(13/32) 47.5)

Learn how to simplify the expression (5 - log_2 13)(log_(32/13) 95 + log_(13/32) 47.5) step-by-step, involving key logarithmic properties and the change of base formula. Suitable for Grades 9-12.

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