logarithm

Meanings

• noun

  A mathematical function that calculates the power to which a number called the base must be raised to produce a given number, called the argument.

• The inverse of the exponential function.

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Synonyms

log

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Variants

List of all variants of logarithm that leads to same result
logarithm , logarithmic , logarithmically , logarithms , common logarithm , common logarithms , Napierian logarithm , Napierian logarithms , natural logarithm , natural logarithms

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Etymology

origin and the way in which meanings have changed throughout history.

Derived from the Greek word 'logos' meaning 'word' or 'meaning' and 'arithmos' meaning 'number'.

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Trivia

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1. The first known use of logarithms was by the Chinese mathematician Chang Heng in the 3rd century AD.

2. John Napier is often credited with inventing logarithms in the late 16th century, but there is evidence that they were used earlier in India and China.

3. Logarithms were used extensively by Isaac Newton and Gottfried Leibniz in their development of calculus.

4. The logarithmic scale is used in many fields, including finance (stock market indices), geology (Richter scale for measuring earthquakes), and music (decibels for measuring sound intensity).

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Related Concepts

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1. Exponential function: A mathematical function where the output is a constant multiplied by the input raised to a power. Logarithms are the inverse of exponential functions.

2. Base: The number to which a power is raised in a logarithmic equation. The most common base is 10, but other bases such as e (approximately 2.71828) can also be used.

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Culture

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Logarithms have been used since ancient times to perform complex mathematical calculations, especially before the invention of electronic calculators. They have been used extensively in science, engineering, and mathematics. In literature, logarithms have been used as plot devices in novels and as metaphors for complex concepts.

How to Memorize "logarithm"

1. visualize
   

   - Visualize a number line with logarithmic scales. Imagine moving along the line as the numbers increase, but the intervals between the numbers get smaller and smaller. This can help you understand how logarithms compress large numbers into smaller ones.

2. associate
   

   - Associate logarithms with the concept of compressing large numbers into smaller ones. For example, you could think of logarithms as a way to squeeze a long number into a shorter one.

3. mnemonics
   

   - Use the mnemonic 'Lots Of Good Apples Help Us Remember Logarithms' to remember the definition: 'Logarithms are a function that gives you the power to which a base number must be raised to get a given number.' The acronym LOGO helps remember 'Logarithms, Order of Growth, and Other Functions'.

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