Definition

1. Adjective:
   • Relating to or using logarithms: Describes something that involves, is based on, or uses logarithms, which are mathematical exponents indicating the power to which a fixed number (the base) must be raised to produce a given number.
   • Having a scale or progression that uses logarithms: Describes a scale, axis, or relationship where values increase by factors (multiplication) rather than by constant additions, making it useful for representing data that spans a very wide range.

Usage Examples

• Adjective:
  • The scientist used a logarithmic scale to plot the earthquake magnitudes, as they vary so dramatically in energy.
  • To solve this equation, you need to apply a logarithmic transformation to both sides.
  • The response of the human ear to sound intensity is approximately logarithmic.

Advanced Usage

• "logarithmic function": A mathematical function, typically written as , which is the inverse of an exponential function.
  • The derivative of a logarithmic function is inversely proportional to its argument.
• "logarithmic scale": A scale of measurement where each tick mark on an axis is the previous tick mark multiplied by a constant value, compressing a wide range of quantities.
  • The pH scale for acidity and the Richter scale for earthquakes are both logarithmic scales.

Variants and Related Words

• Logarithm (n): The exponent to which a base must be raised to yield a given number. Example:
• Log (n, informal): A common abbreviation for logarithm, especially in contexts like "natural log" (ln).
• Logarithmically (adv): In a way that relates to or uses logarithms.
  • The population grew logarithmically over the first century.

Synonyms

• Exponential (Note: This is often an antonym in function, but is closely related as the inverse concept): Involving an exponent or exponents.
• Non-linear: Not arranged in a straight line or involving a constant rate of change (logarithmic relationships are a specific type of non-linearity).

Related Phrases and Concepts

• Logarithmic spiral: A self-similar spiral curve often found in nature, like a nautilus shell.
  • The galaxy's arms often approximate a logarithmic spiral.
• Log-log plot: A graph where both the x and y axes use logarithmic scales.
  • A log-log plot can help determine if data follows a power law.

Adjective

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