Exponentials & Logarithms

Euler’s number, $\mathrm{e}$

In this chapter, we will frequently encounter the mathematical constant $\mathrm{e}\approx \mathrm{2.718.}$ This irrational number is the base of the natural logarithm and appears naturally in many growth and decay models.

Tip: $\mathrm{e}$ will behave just like any number like $\pi$ or $2$ in your calculations. For example

• solving $3x-5=\mathrm{e}$ will follow the same rules as solving $3x-5=2,$
• simplifying ${\displaystyle \frac{{\mathrm{e}}^x}{{\mathrm{e}}^3}}$ will follow the same rules as simplifying ${\displaystyle \frac{2^x}{2^3}.}$