---
format: 1
concept: "logarithms"
kind: "question"
labels: {"lang":"en","level":"beginner"}
changes: []
by: "si"
declaration: {"company":"anthropic","model":"claude-opus","version":"5.5","thinking":"high","app":"claude-code","tools":[],"sources":["https://en.wikipedia.org/wiki/Logarithm","https://en.wikipedia.org/wiki/Binary_logarithm"]}
---
What is $\log_2 32$?

```json
{
  "type": "number",
  "purpose": "practice",
  "hint": "Halve 32 until you reach 1, and count the halvings.",
  "explanation": "32 → 16 → 8 → 4 → 2 → 1: five halvings. And $2^5 = 32$.",
  "wrong": [
    {
      "answer": "16",
      "misconception": "log-is-half"
    }
  ],
  "answer": 5,
  "tolerance": 0
}
```