Log y= 2.5 log x + 0.477
Where log X ranges from [-50,50] steps of 10  give me values of corresponding log y

To clarify, logarithms are only defined for positive values of \( x \). If we try to take the logarithm of a non-positive number (including negative numbers and zero), it results in an undefined value.

Given this, the only valid values for \( \log x \) occur when \( x \) is positive. Let's compute \( \log y \) values for positive values of \( \log x \) within the given range.

Let me recalculate based on that clarification.Here are the corresponding values of \( \log y \) for \( y = 2.5 \log x + 0.477 \) as \( \log x \) ranges from \([-50, 50]\) with steps of 10:

1. \( \log x = -50 \), \( \log y = -124.523 \)
2. \( \log x = -40 \), \( \log y = -99.523 \)
3. \( \log x = -30 \), \( \log y = -74.523 \)
4. \( \log x = -20 \), \( \log y = -49.523 \)
5. \( \log x = -10 \), \( \log y = -24.523 \)
6. \( \log x = 0 \), \( \log y = 0.477 \)
7. \( \log x = 10 \), \( \log y = 25.477 \)
8. \( \log x = 20 \), \( \log y = 50.477 \)
9. \( \log x = 30 \), \( \log y = 75.477 \)
10. \( \log x = 40 \), \( \log y = 100.477 \)
11. \( \log x = 50 \), \( \log y = 125.477 \)

Would you like to explore further or need any additional information?

Here are five related questions for further exploration:
1. How would the equation change if the coefficient of \( \log x \) was altered?
2. What happens to \( \log y \) as \( \log x \) approaches a large negative value?
3. What is the significance of the constant \( 0.477 \) in this equation?
4. Can you plot the function \( \log y \) versus \( \log x \)?
5. How would the function behave if the constant term was negative?

**Tip:** When calculating with logarithms, ensure you distinguish between the logarithm of a variable and the variable itself.

Explore how to calculate logarithmic values for the equation y = 2.5 log(x) + 0.477 across a range of x values from -50 to 50. Understand the behavior of logarithmic functions and their applications in mathematical modeling. Suitable for advanced high school students and beyond.

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