Common Logarithms
Common logarithms are logarithms with base 10. $$ x = \log_{10} a $$
Common logarithms were introduced by the English mathematician Henry Briggs in the early 17th century and quickly became an essential tool in mathematics, astronomy, navigation, and engineering.
You may notice that different textbooks use different symbols for common logarithms.
In many math books, the symbol log without an explicit base refers to a common logarithm, while the symbol ln is used for natural logarithms.
$$ x = \log a $$
Note. This notation became standard because common logarithms were the first logarithms to be used extensively in scientific calculations. Early logarithmic tables were based on powers of ten, making calculations much faster long before electronic calculators existed. Natural logarithms were introduced later by Euler. For centuries, common logarithms were the most widely used type of logarithm, and they are still important today in science and engineering.
Other textbooks write the base explicitly as log10 because they use the symbol log without a base to represent natural logarithms instead.
$$ x = \log_{10} a $$
For this reason, it is always important to check which notation your textbook uses for natural logarithms in order to avoid confusion.
Examples
The common logarithm of 1000 is equal to 3 because 1000 is the third power of 10.
$$ \log_{10} 1000 = 3 $$
Indeed,
$$ 10^3 = 1000 $$
Similarly, the common logarithm of 0.01 is equal to -2 because
$$ 10^{-2} = 0.01 $$
therefore
$$ \log_{10} 0.01 = -2 $$
And so on.
