Log Calculator
Calculate logarithms and antilogarithms with any base. Supports natural log, common log, binary log, and custom bases with detailed explanations.
Logarithm Calculator
Calculate log_b(x) - find the exponent
Calculating: log10(x)
"To what power must 10 be raised to get x?"
Understanding Logarithms
What is a Logarithm?
A logarithm answers the question: "To what power must the base be raised to get this number?"
logb(x) = y ⟺ by = x
"b to the power of y equals x"
Common Logarithm Bases
Natural Logarithm (ln): Base e ≈ 2.718281828
Used in calculus and natural processes
Common Logarithm (log): Base 10
Used in science and engineering
Binary Logarithm (log₂): Base 2
Used in computer science and information theory
Key Properties
- logb(1) = 0 for any base b
- logb(b) = 1 for any base b
- logb(x) is only defined for x > 0
- The base b must be positive and not equal to 1