The *‘logarithm of \(x\) to base \(b\)’* is what you have to raise \(b\) to the power of in order to get \(x\). In symbols, \[\log_b x=a \iff b^a=x.\] Here, \(b\) is a positive real number other than \(1\) and \(x\) is a positive real number.

Being closely related to powers (indices), there are logarithm laws corresponding to the index laws.