It must be read where \(\log x = 0\), in other words, where \(x = 1\). In that case, you couldn't read the \(y\) intercept right off the graph. After all, your values of \(x\) might have been between 10 and 100, so you would have started your horizontal axis at 10. Suppose the horizontal axis didn't start at 1, and there's no need that it should. \(a = slope = \frac \) and note that the units for both \(y\) and \(x\) were given as metres. In the right-hand column, I've looked up the natural logarithms of \(N/N_0\) Panel 3 You can watch it here, Sal Khan explains this much better than me.In the table of values above \(N/N_0\) obeys an exponential relationship. This real-world example was taken from a video of Khan Academy. This should give you an idea of how the effect of earthquakes increases as the magnitude increases. Or in other words, ~5000 times stronger than the East Coast earthquake… If we do the same calculations for this one, we will find that it is 3 times stronger than the one in Japan. Now, the strongest earthquake on record, the Chilean earthquake had a magnitude of 9.5. So, the Japanese earthquake was 100 times stronger than Loma Prieta and 1600 times stronger than one on the East Coast. So to find the difference between this one and Loma Prieta, we take their magnitude differences and raise 10 to that power which is 10^(9.0–7.0) = 100. Also, because of this earthquake, the island of Japan actually got 13 feet wider. The damage it caused was so immense, especially on the Fukushima nuclear power plant. Now, the Tohoku earthquake, one of the deadliest and saddest earthquakes in history, had a magnitude of 9.0. (According to a reporter, who felt the earthquake, she saw cars jumping up and down). That is one big earthquake because imagine the effect of using a strength 16 times higher than the power you need to shake a chair with a person. So, Loma Prieta earthquake was 16 times stronger than the East Coast EQ. So, the 1.2 difference between 7.0 and 5.8 really equals 10 raised to 1.2th power which equals roughly 16. Because remember that our scale was of base 10 logarithmic and in logarithmic scales, moving a distance means multiplying in value. Now, to find the difference in magnitude between Loma Prieta EQ, we cannot just subtract the magnitudes. The East Coast EQ cost just about 200 million dollars in damage and think of its magnitude as the strength you need to roughly shake your chair with a person in it. Thinking about the magnitudes of these earthquakes linearly would be deeply wrong. For base 5, 1 will still be 0 cm, 5 will be above 1 cm, 25 above 2 cm, etc.: If we change the base, the centimeters, or the points on the ruler won’t change only the values of the points above will. For example, in base 10, 1 would be above 0 cm, 10 would above 1 cm, 100 above 2 cm, and so on. In this case, the distance between each point in the logarithmic scale will be 1 cm regardless of the base. Imagine that you put a ruler below your log axis so that 0 cm is directly below 1. How do I move between two random points in a logarithmic line?.How do I plot numbers which are not powers of 10?.Well, the logarithm function will come into play when we start asking questions such as: Now, you might be thinking, ‘where the hell are all the logarithms?’. #LOGARITHMIC GRAPH HOW TO#We will see how to plot in log scale in detail in a later section. #LOGARITHMIC GRAPH CODE#Note that I am not showing the code of plots yet, because I don’t want to mix the explanation of the code and log scale in a single section. The above plot does not obscure any data and can easily plot numbers from 1 to 10 million in a much shorter axis length, courtesy of logarithms.
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