Logarithm Formula

A logarithm tells you the exponent required to raise a base to a specified number. In logarithmic form, log_b(x) = y means bʸ = x, where b is positive and not equal to 1 and x is positive.

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(xᵏ) = k log_b(x)

Change of Base

log_b(x) = log(x) ÷ log(b), using any consistent logarithm base.