A decimal logarithm (also called the common logarithm) is a logarithm with base 10. It is widely used in scientific and engineering calculations. The decimal logarithm of a number \( N \) is denoted by \( \log_{10} N \) or simply \( \lg N \).
\[ \log_{10} N = \lg N \quad (b = 10) \]
This formula defines the decimal logarithm. When the base is 10, we write \( \log_{10} N \) as \( \lg N \).
\[ \lg N = x \quad \text{implies} \quad 10^x = N \]
This is the inverse property of logarithms. If \( \lg N = x \), then raising 10 to the power of \( x \) gives \( N \).