Common Logarithms

What is a Common Logarithm?

A common logarithm is a logarithm with a base of 10.

For all positive numbers $LaTeX: x,\:$ $x,\:$

$LaTeX: \log x=\log_{10}x$ $\log x=\log_{10}x$ .

How To Evaluate a Common Logarithm Using a Calculator

A calculator with a log key can be used to find the base 10 logarithm of any

positive number.

Examples

Use a calculator to find the values of

log 1000, log 142, and log 0.005832.

Solutions

The figure shows that the exact value of log 1000 is 3 (because 10 cubed is 1000), and that log 142 is approximately 2.152288344 and log 0.005832 is approximately -2.234182485.

Calculator Screen showing some common logarithms being evaluated.PNG

Most common logarithms that appear in calculations are approximations.