Mathematics (AS)·Logarithmic and exponential functions · NSSCAS 2.2.2
eˣ and ln x
Narrated lesson · press play
Meet e, the natural growth number, and its partner the natural logarithm, ln x. You will be able to define both, draw their graphs as mirror images in y = x, and use the key facts e⁰ = 1, ln 1 = 0 and ln e = 1. Best of all, you will solve equations like 2ˣ = 20 and e^(2x) = 7 by taking logs, handle disguised-quadratic exponentials, and solve inequalities without falling for the sign-flip trap.
What you'll learn in this lesson
By the end you should be able to (NSSCAS Mathematics (AS) 2.2.2):
- Interpret the definition and properties of eˣ and ln x, including their inverse relationship and their graphs as reflections in y = x.
- Use logarithms to solve equations of the form aˣ = b and related inequalities, including disguised-quadratic exponential equations.
Loading your lesson…
You're watching a free 3-minute preview — create a free account to keep going.