e
High School
Definition
e in mathematics is the base of the natural logarithm. Its has an approximate value that is equal to 2.71828 and is one of the most important constants since it appears in a wide variety of problems. Most commonly, e is seen when dealing with exponential models and exponential functions.
Worked examples
\(e \approx 2.71828\)
The constant e is irrational — the decimal never repeats or terminates.
\(f(x) = e^x\)
The natural exponential function has base e and is its own derivative.
\(A = Pe^{rt}\)
Continuous compound interest uses e to model growth over time t at rate r.
Common mistakes
- \(e = 2.7\) → \(e \approx 2.71828\) Using too few digits can cause significant rounding errors in calculations.
- \(e^x = x \cdot e\) → \(e^x\) is exponential, not linear e raised to x is not multiplication; it's an exponential function where e is the base.
- \(\ln(e) = e\) → \(\ln(e) = 1\) The natural log of e equals 1 because ln is the inverse of the exponential with base e.
Where you'll use it next
You'll use e throughout calculus when differentiating and integrating exponential functions, solving differential equations, and modeling continuous growth and decay in biology, physics, and finance.
Found in 1 StudyPug lesson
Natural log: ln
11th Grade11thAlgebra 2
See also
Reviewed by Pat Cheng, M.Ed. — StudyPug Curriculum Lead · Last updated June 6, 2026