2f: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}`}30:[] 2d:{"title":"Logarithms","cells":[{"id":0,"value":"$2f","pinned":false,"hidden":false,"mode":"md"},{"id":27,"value":"Plot.plot({\n y: {\n grid: true\n },\n marks: [\n Plot.ruleY([0]),\n Plot.ruleX([0]),\n Plot.lineY(data, {\n x: \"x\", \n y: \"y\",\n //marker: \"circle\",\n stroke: \"steelblue\",\n strokeWidth: 3,\n title: (d) => `(${(d.x).toLocaleString(undefined, {minimumFractionDigits: 3})}, ${(d.y).toLocaleString(undefined, {minimumractionDigits: 3})})`\n })\n ]\n})","pinned":false,"hidden":false,"mode":"ojs"},{"id":135,"value":"
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