## Introduction to Logarithmic Functions

In $2010$, a major earthquake struck Haiti, destroying or damaging over $285,000$ homes.[1] One year later, another, stronger earthquake devastated Honshu, Japan, destroying or damaging over $332,000$ buildings,[2] like those shown in the picture above. Even though both caused substantial damage, the earthquake in $2011$ was $100$ times stronger than the earthquake in Haiti. How do we know? The magnitudes of earthquakes are measured on a scale known as the Richter Scale. The Haitian earthquake registered a $7.0$ on the Richter Scale[3] whereas the Japanese earthquake registered a $9.0$.[4]

The Richter Scale is a base-ten logarithmic scale. In other words, an earthquake of magnitude 8 is not twice as great as an earthquake of magnitude $4$. It is ${10}^{8 - 4}={10}^{4}=10,000$ times as great! In this lesson, we will investigate the nature of the Richter Scale and the base-ten function upon which it depends.