Logarithm Calculator
Calculate logarithms with any base including natural log (ln), common log (log₁₀), and custom bases
Logarithm Calculator
Logarithm Reference
Basic Definition
log₍ᵦ₎(x) = y ⟺ b^y = x
"b to what power equals x?"
Common Logarithms
ln(x)Natural log (base e)
log₁₀(x)Common log (base 10)
log₂(x)Binary log (base 2)
Logarithm Properties
log₍ᵦ₎(xy) = log₍ᵦ₎(x) + log₍ᵦ₎(y)
log₍ᵦ₎(x/y) = log₍ᵦ₎(x) - log₍ᵦ₎(y)
log₍ᵦ₎(x^n) = n·log₍ᵦ₎(x)
log₍ᵦ₎(b) = 1
log₍ᵦ₎(1) = 0
Change of Base Formula
log₍ₐ₎(x) =
log₍ᵦ₎(x)
log₍ᵦ₎(a)
Special Values
ln(e) = 1
log₁₀(10) = 1
log₂(2) = 1
ln(1) = 0
log₁₀(100) = 2
log₂(8) = 3
Frequently Asked Questions
A logarithm is the inverse operation of exponentiation. log₍ᵦ₎(x) = y means that b^y = x. For example, log₍₂₎(8) = 3 because 2³ = 8. Logarithms help solve exponential equations and are used in many scientific applications.
Tips
- Enter the dimensions in the same unit for consistency.
- Results update automatically as you type.
- Use the unit selector to convert between different measurement systems.