Section 4.4 Logarithmic Scales

Plot the distances on a number line Object Distance (million km) Mercury 58 Venus 108 Earth 149 Mars 228 Jupiter 778 Saturn 1426 Uranus 2869 Neptune 4495 Pluto 5900 Proxima Centauri 4.1 x 107 Andromeda Galaxy 2.4 x 1013

What we have created is a logarithmic scale If you haven’t already, try plotting the data on an axis labeled 100, 101, 102, 103, and so on How do you decide where to put each planet on this scale? Can we fit all the planets now? In order to fit all the planets on this scale you must convert their distances to powers of 10 How do we do this? Recall What we have created is a logarithmic scale

Use of logs to fit an exponential function to data Consider the following table of data Create a scatter plot with your calculator What form does the data have? x y 1 210 2 405 3 833 4 1590 5 3245 6 6510

We can use logarithms to make this data linear Make a scatter plot of x vs. ln(y) How does the data look? Find both the exponential and linear regression functions x y ln(y) 1 210 5.34 2 405 6 3 833 6.72 4 1590 7.37 5 3245 8.08 6510 8.78

In your groups try problems 12 and 15