Slow Is Not the Same as Stopped

You'll learnto walk the anatomy of a logarithmic curve and see that it never levels off.

The log curve flattens as it goes — and half the class concludes it levels off. It never does. Walk its anatomy: the anchor at (1, 0), the height that reads off an exponent, the vertical wall at x = 0, and the patient climb that eventually passes any ceiling you draw, even if height 100 takes until x = 2¹⁰⁰.

8 STEPS · 6 QUICK CHECKS · y = log₂x · v2

y = log₂x

Before you start

What you're looking at

Powers of 2 and their logs plotted as points — (1,0), (2,1), (4,2), (8,3) — before the full curve appears.

The question

The curve keeps flattening — does it ever stop climbing?

Watch for

The anchor at (1,0), the wall at x = 0, and a climb that eventually passes any ceiling you draw.

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