====== Logarithm ======



<tabbox Intuitive> 


  
<blockquote>Given how the natural log is described in math books, there’s little “natural” about it: it’s defined as the inverse of $e^x$, a strange enough [[basic_tools:exponential_function|exponent]] already.

But there’s a fresh, intuitive explanation: The natural log gives you the time needed to reach a certain level of growth.
<cite>[[https://betterexplained.com/articles/demystifying-the-natural-logarithm-ln/|Demystifying the Natural Logarithm (ln)]] by Kalid Azad</cite></blockquote>
<tabbox Concrete> 

  * The best introduction is [[https://betterexplained.com/articles/demystifying-the-natural-logarithm-ln/|Demystifying the Natural Logarithm (ln)]] by Kalid Azad
  * See also [[https://betterexplained.com/articles/think-with-exponents/|How To Think With Exponents And Logarithms]] by Kalid Azad and [[https://betterexplained.com/articles/using-logs-in-the-real-world/|Using Logarithms in the Real World]] by Kalid Azad
 
<tabbox Abstract> 
Some things go up really fast, like the number of cases of coronavirus in March.  Some things go down really fast, like the stock market in March.

Logarithms are a way to flatten exponential curves, so we can see and understand their structure, even when dealing with extreme/exponential growth.

<note tip>
The motto in this section is: //the higher the level of abstraction, the better//.
</note>

  
<tabbox Why is it interesting?> 


</tabbox>