Lesson 9 of 48
Exponents and their inverse
Repeated multiplication, and the question that forces you to invent logarithms.
“How many times do I multiply to get here?” has no answer in the language of multiplication, so you build a new one. Compute cost, model scaling and information all live on this axis.
Do this
Without a calculator, justify that 2^10 is a little over 1000. Then use that single fact to estimate 2^20 and 2^30, and say how far off you expect to be.
The question that unlocks the next lesson
Given 2^10 ≈ 1000, roughly what is 2^30?
- Aabout 3,000
- Babout 30,000
- Cabout a billion
- Dabout a million