The common logarithm

Summary

\[{10}^a=c\]

has a unique solution \(a\) .
The solution \(a\) is denoted by \(log c\) and pronounced the common logarithm of \(c\) or simply the logarithm of \(c\) if it is understood that it is the common one.
For example, \(log 100=log {10}^2=2\) and \(log 0.01=log {10}^{-2}=-2\) .
If \(c≤0\) then \(log c\) is not defined.
The common logarithm of \(c\) is also called the logarithm to base 10 of \(c\) denoted by \({log}_{10} c\) .