Common Logarithm of a Number
Exponent to which the number 10 must be raised to obtain a given number.
- Consider the expression [latex]\log_{10}(649) ≈ 2.812[/latex]. The characteristic (the integer part of the logarithm) is 2, and the mantissa is 0.812, or 2.812 – 2 = 0.812.
- Consider the expression [latex]\log_{10}(3.779) ≈ 0.577[/latex]. The characteristic (the integer part of the logarithm) is 0, and the mantissa is 0.577, or 0.577 – 0 = 0.577.
Notation
If [latex]a[/latex] = 10[latex]^{n}[/latex], then [latex]n[/latex] is the common logarithm of [latex]a[/latex] to the base 10. This relationship is written as: [latex]n = \log_{10}(a)[/latex] which is read as "[latex]n[/latex] is equal to the logarithm of [latex]a[/latex] to the base 10".Examples
- If log[latex]_{10}(100) = 2[/latex], then 100 = 10[latex]^{2}[/latex].
- If log[latex]_{10}(1000) = 3[/latex], then 1000 = 10[latex]^{3}[/latex].