The natural logarithm is the logarithm to the base $e$, where $e$ is an irrational and transcendental number approximately equal to 2.71828. It is commonly denoted as $\ln(x)$.
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The natural logarithm of a positive number $x$ is written as $\ln(x)$.
The base $e$ of the natural logarithm is approximately equal to 2.71828.
$\ln(e) = 1$ and $\ln(1) = 0$ are key properties.
The derivative of $\ln(x)$ with respect to $x$ is $\frac{1}{x}$.
The natural logarithm function is the inverse of the exponential function $e^x$.
Review Questions
What is the value of $\ln(e)$?
What does the natural logarithm function represent?
How do you express the natural logarithm of a product using properties of logarithms?
Related terms
Exponential Function: A mathematical function in the form $f(x) = e^x$, where $e$ is Euler's number.
Logarithmic Function: A function that uses a logarithm, typically written as $\log_b(x)$ for a given base $b$. The natural log specifically uses base $e$.
Euler's Number: An irrational and transcendental number approximately equal to 2.71828, often denoted as $e$. It serves as the base for natural logarithms.