logarithmic

/,lɔgə'riθmik/

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Word: Logarithmic

Part of Speech: Adjective

Basic Definition: The word "logarithmic" refers to something that relates to or uses logarithms. Logarithms are mathematical functions that help to solve problems involving exponential growth or decay.

Simple Explanation: When we say something is "logarithmic," we are often talking about a way to scale or measure things that grow or shrink very quickly. Logarithms can make it easier to understand those large changes.

Usage Instructions:

• You can use "logarithmic" when discussing math, science, or any context where growth and decay are involved.
• It often appears in phrases like "logarithmic scale" or "logarithmic function."

Examples:

1. Basic Example: "The population of the city grew on a logarithmic scale, meaning it increased very rapidly over a short time."
2. Mathematical Example: "The logarithmic function helps us find the time it takes for a certain amount of money to double in a bank account with compound interest."

Advanced Usage:

• In advanced mathematics, a logarithmic function is often written as ( y = \log_b(x) ), where ( b ) is the base of the logarithm, and ( x ) is the number you are taking the logarithm of.
• Logarithmic scales are commonly used in scientific measurements, such as the Richter scale for earthquakes or the decibel scale for sound intensity.

Word Variants:

• Logarithm (noun): The mathematical function itself.
• Logarithmically (adverb): In a manner that relates to logarithms.

Different Meanings:

• In mathematics, "logarithmic" has a specific meaning, but it can also be used metaphorically in other fields, such as describing data trends that appear to grow or shrink rapidly.

Synonyms:

• Exponential (in some contexts, but be careful as they are not exactly the same)
• Scale (when referring to measurements)

Idioms and Phrasal Verbs:

• There aren't specific idioms or phrasal verbs directly related to "logarithmic," but in discussions about growth, you might hear phrases like "grow exponentially," which is related but not the same.

Summary:

"Logarithmic" is an important term in mathematics that helps us understand how things change over time, especially when those changes are very large or very small.

Academic

Adjective

1. of or relating to or using logarithms
   • logarithmic function