Logarithm Calculator
Calculate logarithms with any base. Convert between log, ln, and log10. Apply log properties.
Exponential & Logarithm Curves
LogarithmExponential
Results
log10(100)
2.000000
4.605170
ln (base e)
2.000000
log10
6.643856
log2
Logarithm Properties
Product Rule
log_b(xy) = log_b(x) + log_b(y)
Quotient Rule
log_b(x/y) = log_b(x) - log_b(y)
Power Rule
log_b(x^n) = n × log_b(x)
Change of Base
log_b(x) = log_c(x) / log_c(b)

Key Formulas

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

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