Logarithm Calculator - Calculate log(x)
Result:
Welcome to our Logarithm Calculator. This tool calculates logarithms with any base, including common logarithms (base 10), natural logarithms (base e), and custom bases.
What is a Logarithm?
A logarithm is the inverse of exponentiation. log₍ᵦ₎(x) asks "what power must b be raised to get x?"
Understanding Logarithms
Logarithms are the inverse operation of exponents:
If b^y = x, then log₍ᵦ₎(x) = y
Common Types
Common log: log₁₀(x) or log(x)
Natural log: logₑ(x) or ln(x)
Binary log: log₂(x)
Custom base: logᵦ(x)
Properties
log(xy) = log(x) + log(y)
log(x/y) = log(x) - log(y)
log(x^n) = n·log(x)
log(1) = 0, log(base) = 1
Applications of Logarithms
- Scientific calculations: pH scale, Richter scale
- Computer science: Algorithms complexity
- Finance: Compound interest calculations
- Statistics: Data transformations
Examples
Common Log
log₁₀(100) = 2
10² = 100Natural Log
ln(e) = 1
e¹ = e ≈ 2.718Binary Log
log₂(8) = 3
2³ = 8Find Calculator
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