Logarithm Calculator

Calculate logarithms step by step with explanations and graph analysis.

Enter Logarithm Values

Logarithm: log₁₀(100)

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About Logarithms

What is a Logarithm?

A logarithm is the inverse operation to exponentiation. It answers the question: "To what power must the base be raised to get a given number?" The logarithm of a number x to base b is written as log_b(x).

Common Logarithm Properties

  1. Product Rule: log_b(xy) = log_b(x) + log_b(y)
  2. Quotient Rule: log_b(x/y) = log_b(x) - log_b(y)
  3. Power Rule: log_b(x^n) = n log_b(x)
  4. Change of Base: log_b(x) = log_c(x) / log_c(b)

Applications in Real Life

  • Sound intensity and decibel scales
  • Earthquake magnitude (Richter scale)
  • pH scale in chemistry
  • Computer science and information theory

Frequently Asked Questions

What is the natural logarithm?

The natural logarithm (ln) uses base e (approximately 2.718) and is commonly used in calculus and natural sciences.

What is the common logarithm?

The common logarithm uses base 10 and is often written as log(x) without specifying the base.