https://youtu.be/M-N2PQ5UZns

In this video I go over logarithms but this define natural logarithms using integrals through the Fundamental Theorem of Calculus. In my previous videos I went over the definition of the logarithm as an inverse to the exponential function but the definition I go over in this video is more concrete and better suited when dealing with derivatives and integrals.

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# Natural Logarithms Defined as Integrals: Introduction

![Natural Log as Integrals Intro.jpeg](https://files.peakd.com/file/peakd-hive/mes/zACQS1WR-Natural20Log20as20Integrals20Intro.jpeg)

Previously logarithmic functions were defined as inverse functions to exponential functions:

![image.png](https://files.peakd.com/file/peakd-hive/mes/RbwoNT9g-image.png)

A better definition is to use the Fundamental Theorem of Calculus and go from there. 

**Definition:** 

The Natural Logarithmic function is defined by:

![image.png](https://files.peakd.com/file/peakd-hive/mes/oYvQbQ4j-image.png)

![image.png](https://files.peakd.com/file/peakd-hive/mes/k5NTGMPC-image.png)