--- title: What is a logarithm? - In Mathematics and Their Properties description: What is a logarithm? The exponent that produces a given number from a chosen base. url: https://astra-ai.co/videos/logarithms/logarithm/what-is-a-logarithm/ locale: en type: video-lesson keywords: - logarithm - log definition - common log - exponent question published: 2026-10-01T10:05:15.025Z updated: 2026-10-04T22:01:48.329Z alternates: bg: https://astra-ai.co/bg/videos/logaritmi/logaritam/kakvo-e-logaritam/ br: https://astra-ai.co/br/videos/logaritmos/capitulo-matematica-042/video-matematica-044/ cs: https://astra-ai.co/cs/videos/logaritmy/logaritmus/co-je-logaritmus/ da: https://astra-ai.co/da/videos/logaritmer/logaritme/hvad-er-en-logaritme/ de: https://astra-ai.co/de/videos/logarithmen/logarithmus/was-ist-ein-logarithmus/ el: https://astra-ai.co/el/videos/logarithmoi/logarithmos-kefalaio/what-is-a-logarithm/ en: https://astra-ai.co/videos/logarithms/logarithm/what-is-a-logarithm/ en-IN: https://astra-ai.co/en-IN/videos/logarithms/chapter-25335562/what-is-a-logarithm/ en-PH: https://astra-ai.co/en-PH/videos/logarithms/chapter-25335562/lesson-c82b52ae/ es: https://astra-ai.co/es/videos/logaritmos/logaritmo/que-es-un-logaritmo/ es-AR: https://astra-ai.co/es-AR/videos/logaritmos/capitulo-36/leccion-44/ es-CL: https://astra-ai.co/es-CL/videos/logaritmos/capitulo-36/leccion-de-matematicas-44/ es-PE: https://astra-ai.co/es-PE/videos/logaritmos/capitulo-video-25335562/leccion-de-video-c82b52ae/ et: https://astra-ai.co/et/videos/logaritmid/logaritm/mis-on-logaritm/ fi: https://astra-ai.co/fi/videos/logaritmit/logaritmi/mika-on-logaritmi/ fr: https://astra-ai.co/fr/videos/logarithmes/logarithme/quest-ce-quun-logarithme/ hr: https://astra-ai.co/hr/videos/logaritmi/logaritam/sto-je-logaritam/ hu: https://astra-ai.co/hu/videos/logaritmusok/logaritmus/mi-az-a-logaritmus/ id: https://astra-ai.co/id/videos/logaritma/logaritma/apa-itu-logaritma/ it: https://astra-ai.co/it/videos/logaritmi/logaritmo/cose-un-logaritmo/ ja: https://astra-ai.co/ja/videos/logarithms-ja/36/044/ km: https://astra-ai.co/km/videos/logarithms/chapter-25335562/lesson-c82b52ae/ ko: https://astra-ai.co/ko/videos/logarithms-ko/36/044/ lo: https://astra-ai.co/lo/videos/lo-d4a82fdb/lo-25335562/lo-c82b52ae/ lt: https://astra-ai.co/lt/videos/logaritmai/logaritmas/pamoka-c82b52ae/ lv: https://astra-ai.co/lv/videos/logaritmi/logaritms/stunda-c82b52ae/ ms: https://astra-ai.co/ms/videos/logaritma/bab-42-matematik-asas/pelajaran-044/ ms-BN: https://astra-ai.co/ms-BN/videos/logaritma/bab-25335562/pelajaran-c82b52ae/ mx: https://astra-ai.co/mx/videos/logaritmos/capitulo-36/leccion-44/ my: https://astra-ai.co/my/videos/my-d4a82fdb/my-25335562/my-c82b52ae/ nl: https://astra-ai.co/nl/videos/logaritmen/logaritme/wat-is-een-logaritme/ no: https://astra-ai.co/no/videos/logaritmer/logaritme/hva-er-en-logaritme/ pl: https://astra-ai.co/pl/videos/logarytmy/logarytm/czym-jest-logarytm/ pt: https://astra-ai.co/pt/videos/logaritmos/logaritmo/o-que-e-um-logaritmo/ pt-TL: https://astra-ai.co/pt-TL/videos/logaritmos/capitulo-de-video-036/licao-de-video-044/ ro: https://astra-ai.co/ro/videos/logaritmi/logaritm/lectie-video-c82b52ae/ sk: https://astra-ai.co/sk/videos/logaritmy/kapitola-036/lekcia-044/ sl: https://astra-ai.co/sl/videos/logaritmi/logaritem/kaj-je-logaritem/ sr: https://astra-ai.co/sr/videos/logaritmi/poglavlje-036/lekcija-044/ sv: https://astra-ai.co/sv/videos/logaritmer/logaritm/vad-ar-en-logaritm/ th: https://astra-ai.co/th/videos/lokarithuem/bot-42-lokarithuem/botrian-044/ tr: https://astra-ai.co/tr/videos/logaritmalar/bolum-036/ders-044/ uk: https://astra-ai.co/uk/videos/uk-topic-17/uk-chapter-42/uk-what-is-a-logarithm/ vi: https://astra-ai.co/vi/videos/vi-topic-17/vi-chapter-42/vi-what-is-a-logarithm/ zh-HK: https://astra-ai.co/zh-HK/videos/shuxue-kecheng-017/shuxue-zhang-042/shuxue-kecheng-044/ zh-TW: https://astra-ai.co/zh-TW/videos/logarithms/chapter-25335562/lesson-c82b52ae/ --- # What is a logarithm? > A logarithm answers which exponent produces a given number. This lesson defines it and reads a simple log statement. Logarithms represent a fundamental concept in mathematics, allowing us to view exponential functions from a different perspective. The logarithm of a number _b_ with base _a_, written as logₐb, is the exponent to which the base _a_ must be raised to obtain the number _b_. This concept is crucial for understanding various mathematical and scientific phenomena involving exponential growth or decay. ## **Definition** For any positive number _a_ (where _a_ ≠ 1) and any positive number _b_, the logarithm of _b_ with base _a_ equals _c_ if _a^c = b_. This can be expressed as logₐb = c. ## **Properties of Logarithms** The properties of logarithms—such as the rules for calculating the logarithm of a product, quotient, and power—make it easier to manipulate and solve equations. These properties allow complex expressions to be broken into simpler parts, which is especially useful when solving exponential and logarithmic equations. ## **Types of Logarithms** There are two particularly important types of logarithms: - **Natural logarithm:** Has the base _e_ (Euler’s number, approximately 2.718). Natural logarithms are widely used in advanced mathematics. - **Common logarithm:** Has the base 10 and is often used in scientific contexts. ## **Conclusion** Logarithms are a powerful tool in mathematics that simplify the handling of complex exponential functions. Understanding them enables easier equation solving, function analysis, and modeling of situations involving exponential growth or decay. The basics of logarithms provide a foundation for building more complex mathematical concepts. Mastering their use opens the door to many areas of mathematics and its applications.