Logarithm Calculator

Calculate logarithms, explore their properties, and use the change of base formula. Supports common, natural, and custom bases.

Exponents & Logarithms
Grade 7+
Intermediate

Features

  • Calculate logarithms for any base (including e, 2, 10)
  • Explore product, quotient, power, and root properties
  • Change of base formula support
  • Tabs for different logarithm operations
  • Real-time result display
  • Input validation and error handling

About Logarithms

A logarithm is the power to which a number must be raised to get another number. For example, the logarithm of 100 to the base 10 is 2, because 10² = 100.

Key Logarithm Properties

  • Product Rule: log₍ₐ₎(x×y) = log₍ₐ₎(x) + log₍ₐ₎(y)
  • Quotient Rule: log₍ₐ₎(x÷y) = log₍ₐ₎(x) - log₍ₐ₎(y)
  • Power Rule: log₍ₐ₎(xⁿ) = n × log₍ₐ₎(x)
  • Change of Base: log₍ₐ₎(x) = log₍ᵦ₎(x) ÷ log₍ᵦ₎(a)

Logarithms are used in many fields including mathematics, science, engineering, and finance for tasks like solving exponential equations, analyzing growth and decay, and measuring quantities that vary over a large range.