How to Use the Logarithm Calculator
This calculator supports four modes: custom base log (log_b), natural log (ln), common log (log10), and antilog. Select a mode, enter the base and argument, and the result appears instantly.
Key Formulas
log_b(x) = y means b^y = x (b > 0, b β 1, x > 0)
Natural log: ln(x) = log_e(x), e β 2.71828
Common log: log10(x) = log_10(x)
Change of base: log_b(x) = ln(x) / ln(b)
Common Applications
logβ is used in computer science for bit counting and binary search analysis. pH = βlogββ[HβΊ] in chemistry. Decibels = 10Β·logββ(P/Pβ) in acoustics.
FAQ
The argument of a logarithm must be strictly positive. Zero and negative numbers are undefined in real-number logarithms.
When the argument is not a perfect power of the base, the result is irrational. For example, logβ(5) β 2.3219. The calculator displays up to 10 decimal places.