Logarithm Calculator
Compute logarithm base 10, natural log (ln), or custom bases. Fast, free, and fully client-side.
Calculator Inputs
Value (x)
Log Base
Result—
How the Logarithm Calculator Works
A logarithm is the inverse operation of exponentiation, determining the exponent to which a base number must be raised to yield a given value. Common logarithms use base 10, natural logarithms use base e (Euler number ~2.718), and binary logarithms use base 2.
Formula
log_b(x) = y ⟺ b^y = x
Where b is the positive base (b ≠ 1) and x is the positive real argument.
Calculation Example
log₁₀(1,000) = 3 because 10³ = 1,000. Similarly, log₂(16) = 4 because 2⁴ = 16.
Frequently Asked Questions
What is the change of base formula?
log_b(x) = ln(x) / ln(b) = log₁₀(x) / log₁₀(b), allowing evaluation of any logarithm on standard calculators.
Can you take the logarithm of a negative number?
In real numbers, logarithms are undefined for zero and negative inputs.