Exponential and logarithm
One exponential, read three ways: a mirror across y = x, a straight line on a log axis, and why e is natural.
Exponents and logarithms
4 pieces about this concept, across works, topic guides, and exam visualizations.
Topics
Works
Exponential growth and decay
Exponential growth and decay of y = Ce^(kt), with doubling time, half-life, and slope proportional to height.
Logarithmic scale
A logarithmic scale turns equal ratios into equal steps, so exponential growth becomes a straight line.
Geometric definition of the natural logarithm
Define ln t as the integral of 1/x from 1 to t, and e as the unique positive number with ln e = 1.