The Log Is the Exponential in a Mirror

You'll learnto see the logarithm as the exponential reflected across the line y = x.

Draw y = 2ˣ, fold the plane along the diagonal y = x, and the curve that lands on the far side is log₂x with every point’s coordinates swapped. Every fact about the log falls out of that one fold: its domain, its wall at x = 0, its refusal to level off, and the reciprocal 1/2ˣ that fails the test. Twelve short steps; press Next for each one.

12 STEPS · 6 QUICK CHECKS · y = 2ˣ ⇄ y = log₂x · v3

fold along y = x · the exponential becomes the log

Before you start

What you're looking at

The curve y = 2^x and the diagonal y = x, with a point like (3, 8) about to become (8, 3).

The question

What happens to each point's coordinates when the plane folds along the diagonal?

Step 1 / 12