27:null 28:["$","title",null,{"children":"Logarithms | Kevin Perese | Observable"}] 2d:T40a,# Logarithms Logarithms are [functions](https://observablehq.com/d/5a590d2ad64a4afa). that produce the *inverse* of exponentional functions. Logarithmic functions are typically written in the form: ${tex`log_{b}(x) = y`},

where ${tex`b`} is the *base* for the logarithm.

They are called the *inverse* of exponential functions because:

${tex`log_{b}(b^x) = x`}

Although you could, in theory, use any value you want for the base, ${tex`b`}, in practice there are only three bases that are commonly used: * 10, * 2, * and the mathematical constant ${tex`e`}. ## Some examples ## The Natural Logarithm When the base (${tex`b`}) is equal to ${tex`e`}, the logarithm is referred to as the ***natural logarithm*** and is written as:

${tex`ln(x) = y`}

(It's just **assumed** that you know that the base for the natural logarithm function is ${tex`e`}; so you might as well just memorize this.) ### What's so "natural" about the Natural Logarithm? ${tex`\mathbb{R}^+\longrightarrow\mathbb{R}`}2e:[] 2b:{"id":"3a434857ae2d694d","slug":null,"title":"Logarithms","thumbnail":"8c1aab5d87a25dbc3ccb5ef86ff730bf2aaeb7a1b0e45dd6f9c0a49421190370","access_level":"public","create_time":"$D2023-04-16T21:16:54.048Z","update_time":"$D2023-05-19T21:15:26.078Z","view_time":null,"first_public_time":"$D2023-04-16T21:16:54.048Z","has_unpublished_edits":null,"fork":false,"stars":0,"starred":false,"owner":{"type":"team","id":"1339992d0aa77f13","login":"kevinxperese","name":"Kevin Perese","avatar_url":"https://avatars-next.observableusercontent.com/4c732d05ac7051c3b09a7f7e5bb547d6811a5044e7ce9f63713a8c7d4cbe9450","tier":"starter_2024"},"version":185,"publish_version":null,"role":null,"authored":false,"authors":[{"type":"individual","id":"fed9c6d72cf923a5","login":"kevinxperese","name":"Kevin Perese","avatar_url":"https://avatars-next.observableusercontent.com/4c732d05ac7051c3b09a7f7e5bb547d6811a5044e7ce9f63713a8c7d4cbe9450","tier":null}],"members":[{"type":"individual","id":"fed9c6d72cf923a5","login":"kevinxperese","name":"Kevin Perese","avatar_url":"https://avatars-next.observableusercontent.com/4c732d05ac7051c3b09a7f7e5bb547d6811a5044e7ce9f63713a8c7d4cbe9450","tier":null,"role":"editor"}],"comments":[],"custom_thumbnail":false,"trashed":false,"lapsed":null,"subscribed":null,"forks":0,"collection":null,"type":"notebook","body":{"title":"Logarithms","cells":[{"id":0,"value":"$2d","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":27,"value":"Plot.plot({\n y: {\n grid: true\n },\n marks: [\n Plot.ruleY([0]),\n Plot.ruleX([0]),\n Plot.lineY(data, {\n x: \"x\", \n y: \"y\",\n //marker: \"circle\",\n stroke: \"steelblue\",\n strokeWidth: 3,\n title: (d) => `(${(d.x).toLocaleString(undefined, {minimumFractionDigits: 3})}, ${(d.y).toLocaleString(undefined, {minimumractionDigits: 3})})`\n })\n ]\n})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":135,"value":"
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