The common logarithm

Summary

• For any $c>0$ the equation

$${10}^a=c$$

• 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 ${log}_{10} c$ .