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# 3.8: Common and Natural Logarithms

Difficulty Level: At Grade Created by: CK-12
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Practice Common and Natural Logarithms

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### Vocabulary Language: English

TermDefinition
$e$ $e$ is an irrational number that is approximately equal to 2.71828. As $n \rightarrow \infty, \left(1+ \frac{1}{n}\right)^n \rightarrow e$.
Change of Base Formula Let $b, x,$ and $y$ be positive numbers, $b \ne 1$ and $y \ne 1$. Then, $\log_y x=\frac{\log_b x}{\log_b y}$. More specifically, $\log_y x=\frac{\log x}{\log y}$ and $\log_y x=\frac{\ln x}{\ln y}$, so that expressions can be evaluated using a calculator.
Common Log A common logarithm is a log with base 10. The log is usually written without the base.
Common Logarithm A common logarithm is a log with base 10. The log is usually written without the base.
e $e$ is an irrational number that is approximately equal to 2.71828. As $n \rightarrow \infty, \left(1+ \frac{1}{n}\right)^n \rightarrow e$.
Natural Log A natural logarithm is a log with base $e$. The natural logarithm is written as ln.
Natural Logarithm A natural logarithm is a log with base $e$. The natural logarithm is written as ln.
Transcendental Number A transcendental number is a number that is not the root of any rational polynomial function. Examples include $e$ and $\pi$.

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