Logarithm Calculator

A logarithm answers the question: "To what power must I raise the base to get this number?"

If b^y = x, then log_b(x) = y.

For example: 2³ = 8, so log₂(8) = 3.

Base 10 (common log): Written as log(x) or log₁₀(x). Used in science, engineering, and pH calculations.

Base e (natural log): Written as ln(x). The inverse of e^x. Essential in calculus, growth/decay models, and statistics.

Base 2 (binary log): Written as log₂(x). Used in computer science for algorithm complexity, data structures, and information theory.

" title="

Base 10 (common log): Written as log(x) or log₁₀(x). Used in science, engineering, and pH calculations.

Base e (natural log): Written as ln(x). The inverse of e^x. Essential in calculus, growth/decay models, and statistics.

Base 2 (binary log): Written as log₂(x). Used in computer science for algorithm complexity, data structures, and information theory.

lg b

Base b

Result:

To convert between bases, divide the log in the target base by the log of the original base in the target base:

log_b(x) = ln(x) / ln(b) = log₁₀(x) / log₁₀(b)

The calculator handles this conversion automatically — just enter your number and desired base.