Common logarithm

Definition

A common logarithm is a logarithm with base 10. It is often written as $\log_{10} x$ or simply $\log x$.

5 Must Know Facts For Your Next Test

1. The common logarithm of a positive number $x$ is the exponent to which 10 must be raised to produce $x$.
2. $\log_{10}(1) = 0$ because $10^0 = 1$.
3. $\log_{10}(10) = 1$ because $10^1 = 10$.
4. Common logarithms are used in many scientific and engineering fields due to their simplicity with base-10 calculations.
5. Common logarithms can be calculated using scientific calculators, usually represented by the 'LOG' button.

Review Questions

• What is the common logarithm of 100?
• If $\log_{10}(x) = -2$, what is the value of $x$?
• How do you represent the common logarithm of a number using a calculator?

Related terms

Natural Logarithm: A logarithm with base e, where e is approximately equal to 2.71828. Written as $\ln(x)$.

Exponential Function: A function in which an independent variable appears in the exponent. Represented as $f(x) = a^x$, where \(a >0\).

Logarithmic Function: The inverse function of an exponential function, defined for positive real numbers. Represented as $f(x) = \log_b(x)$ where \(b >0\).