Common logarithm

Definition

A common logarithm is a logarithm with base 10, often denoted as $\log_{10}$ or simply log. It is used to solve equations involving exponential growth or decay where the base of the exponent is 10.

5 Must Know Facts For Your Next Test

1. The common logarithm of 10 is 1, i.e., $\log_{10}(10) = 1$.
2. Common logarithms are used extensively in scientific calculations and engineering due to their simplicity with base 10.
3. The common logarithm of a number can be found using calculators or logarithmic tables.
4. Properties include: $\log_{10}(ab) = \log_{10}(a) + \log_{10}(b)$ and $\log_{10}\left(\frac{a}{b}\right) = \log_{10}(a) - \log_{10}(b)$.
5. Any number raised to the power of its common logarithm returns that number: $10^{\log_{10}(x)} = x$.

Review Questions

• What is the value of $\log_{10}(1000)$?
• How can you express the product of two numbers using their common logarithms?
• Explain why $\log_{10}$ is called the common logarithm.

Related terms

Natural Logarithm: A logarithm with base e (approximately 2.718), denoted as $\ln$. It is widely used in calculus and natural phenomena.

Exponential Function:

$f(x) = a^x$, where a is a positive constant. Exponential functions describe rapid growth or decay.

$e$ (Euler's Number): $e$ is an irrational constant approximately equal to 2.71828, serving as the base for natural logarithms.