.pyplot as plt

Data points

x = [10, 100, 1000, 10000, 100000] y = [0.5, 4.2, 40.1, 400.3, 4002.7]

Plot

plt.figure(figsize=(8, 6)) plt.plot(x, y, marker='o', linestyle='-', linewidth=2, markersize=6) plt.xscale('log') plt.yscale('log') plt.title('Log-Log Plot of Given Points', fontsize=14) plt.xlabel('X Values (log scale)', fontsize=12) plt.ylabel('Y Values (log scale)', fontsize=12) plt.grid(True, which='both', linestyle='--', linewidth=0.5) plt.show()The graph above illustrates the relationship between the given points $(10, 0.5), (100, 4.2), (1000, 40.1), (10000, 400.3), (100000, 4002.7)$ on a log-log scale, showing how $y$ scales with $x$.

Would you like details about the scaling behavior, equations fitting these points, or any additional analysis?

Here are some follow-up questions you might consider:

1. Would you like the data fitted to a mathematical model, such as a power law?
2. Do you need the growth rate or scaling factor calculated from this data?
3. Would you like the graph plotted without logarithmic scaling?
4. Should we analyze residuals or goodness of fit for a chosen model?
5. Do you need a table comparing the original values to transformed (logarithmic) values?

Tip: Log-log graphs are particularly useful for identifying power-law relationships between variables