3.2.1—Log laws

For positive arguments, log(ab)=log a+log b, log(a/b)=log a−log b and log(a^p)=p log a. Change of base converts any legal base to a calculator base.

Record argument restrictions before combining or expanding. A logarithm base must be positive and not equal to 1.

ln[(x−1)^2] can be written 2ln|x−1| for x≠1, not 2ln(x−1) without the domain restriction.

Logarithms do not distribute over addition, and dropping absolute values can exclude valid negative arguments.