---
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"]}
---
If $n$ doubles, what happens to $\log_2 n$?

```json
{
  "type": "choose",
  "purpose": "practice",
  "explanation": "Doubling $n$ means one more halving to get back down to 1, so $\\log_2 n$ goes up by exactly 1.",
  "options": [
    {
      "text": "It goes up by 1",
      "correct": true
    },
    {
      "text": "It doubles too",
      "correct": false,
      "misconception": "log-is-half"
    },
    {
      "text": "It halves",
      "correct": false
    },
    {
      "text": "It stays the same",
      "correct": false
    }
  ],
  "multiple": false
}
```