Xandra Granade 🏳️⚧️ on Nostr: The other piece of math we'll need is the *logarithm function*, which very roughly ...
The other piece of math we'll need is the *logarithm function*, which very roughly maps their input numbers to powers.
In particular, if 𝑎 = log_𝑏(𝑐), then 𝑐 = 𝑏^𝑎. For example, log₁₀(100) = 2, since 10² = 100. Similarly, log₂(32) = 5 since 2⁵ = 32.
(Sometimes I'll just write "log" as shorthand for "log₁₀".)
The logarithm function has some pretty nice properties, including that log(𝑥𝑦) = log(𝑥) + log(𝑦); that is, logarithms turn multiplication into addition.
In particular, if 𝑎 = log_𝑏(𝑐), then 𝑐 = 𝑏^𝑎. For example, log₁₀(100) = 2, since 10² = 100. Similarly, log₂(32) = 5 since 2⁵ = 32.
(Sometimes I'll just write "log" as shorthand for "log₁₀".)
The logarithm function has some pretty nice properties, including that log(𝑥𝑦) = log(𝑥) + log(𝑦); that is, logarithms turn multiplication into addition.