We can use the idea of solving a power equation to find the base of a natural log. Recall the natural log ($\ln$) from your calculator.

1. Enter $\ln\left(2\right)$. You should end up with $\ln\left(2\right)=0.693147\dots$

2. Change this to $\log_b\left(2\right)=0.693147$. Convert your equation from log form to exponent form and solve for the base. Write your answer out to five decimal places.

   This number you just found is called $e$, which is the base of natural log. The number $e$ is an irrational number which is very important in mathematics. You will learn more about this number later in chapter 8.

   Hint (b):

   ${\textit{b}^{0.693147} = 2}$