Logarithm Calculator

Calculate logarithm of a number to any base:

* Use e for scientific notation. E.g: 5e3, 4e-8, 1.45e12

Logarithm expression calculator

Expression with log(value,base):

When:

b^y = x

Then the base b logarithm of a number x:

log_bx = y

Logarithm change of base calculator

Anti-logarithm calculator

In order to calculate log^-1(y) on the calculator, enter the base b (10 is the default value, enter e for e constant), enter the logarithm value y and press the = or calculate button:

When

y = log_bx

The anti logarithm (or inverse logarithm) is calculated by raising the base b to the logarithm y:

x = log_b^-1(y) = b^y

Logarithm rules

Logarithm product rule

log_b(x × y) = log_b(x) + log_b(y)

Logarithm quotient rule

log_b(x / y) = log_b(x) - log_b(y)

Logarithm power rule

log_b(x ^y) = y × log_b(x)

Logarithm base switch rule

log_b(c) = 1 / log_c(b)

Logarithm change of base rule

log_b(x) = log_c(x) / log_c(b)

Logarithm - log(x) ►