Mathematical Logarithm Solver

Log Calculator

Solve logarithms with any base — enter any two values to find the third

Logarithm Equation Solver

Enter any two values to calculate the third in the equation logb(x) = y. Use "e" as base for natural log.

logb(x) = y
Base (b) or "e" for natural log
Argument (x)
Result (y)

Common Logarithms

Quick reference for standard logarithm values.

log(1) = 0
log(10) = 1
ln(1) = 0
ln(e) = 1
log₂(2) = 1
log₂(8) = 3
log(0) = undefined
ln(e²) = 2

Logarithm Rules & Properties

logb(x × y) = logb(x) + logb(y)
Log of a product equals sum of logs
logb(x / y) = logb(x) - logb(y)
Log of a quotient equals difference of logs
logb(xy) = y × logb(x)
Exponent can be pulled out front
logb(1) = 0
Any base log of 1 equals zero
logb(b) = 1
Log of base equals one
Change of base: logb(x) = logk(x) / logk(b)
Convert to any base