Logarithm & Exponent Calculator

Calculate logarithms, natural log, antilog, and exponents with any base

Select Operation

Choose the type of calculation

Input Values

Enter values for logarithm calculation

The number to find the logarithm of (must be positive)

Common bases: 10 (common log), 2 (binary), e ≈ 2.718 (natural)

Common Logarithms

log₁₀(10) = 1
Common logarithm of 10
log₁₀(100) = 2
Common logarithm of 100
log₁₀(1000) = 3
Common logarithm of 1000
ln(e) = 1
Natural log of e ≈ 2.718
log₂(8) = 3
Binary logarithm of 8
log₂(1024) = 10
Binary logarithm of 1024

About Logarithms & Exponents

Logarithm: If b^y = x, then log₍ᵦ₎(x) = y. The logarithm answers: "To what power must we raise the base to get this number?"

Natural Log (ln): Logarithm with base e ≈ 2.71828. Widely used in calculus, physics, and exponential growth/decay.

Antilog: The inverse of logarithm. If log₍ᵦ₎(x) = y, then antilog₍ᵦ₎(y) = x. Calculates b^y.

Exponent: Repeated multiplication. a^n means multiply 'a' by itself 'n' times. Negative exponents give reciprocals.

Properties:
  • log(xy) = log(x) + log(y)
  • log(x/y) = log(x) - log(y)
  • log(x^n) = n × log(x)
  • log₍ᵦ₎(b) = 1, log₍ᵦ₎(1) = 0