Phase 2 · Math, when you need it · Calculus
Exponentials and logarithms
Growth, decay, and why logs turn products into sums.
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Why it matters
Exponentials describe anything that compounds: a list growing 5% a month, interest, viral sharing, and the scores inside softmax. Logarithms undo them, and they have a property machine learning depends on: they turn multiplication into addition. A language model's training loss is a log, perplexity is an exponential, and every probability calculation over long text is done in logs to avoid numbers too small for a computer to store.
What you'll be able to do
- Model compounding growth and decay with exponentials
- Use logarithms as the inverse: 'what power gives this number?'
- Apply the log rules, especially log of a product = sum of logs
- Explain why models add log-probabilities instead of multiplying probabilities
Before this lesson
Next in this phase: Derivatives