A logarithmic function is the inverse of an exponential function, typically written as $f(x) = \log_b(x)$ where $b$ is the base. Common bases include base 10 (common logarithm) and base e (natural logarithm).
5 Must Know Facts For Your Next Test
The natural logarithm, denoted as $\ln(x)$, has a base of $e \approx 2.71828$.
The derivative of $\ln(x)$ is $\frac{1}{x}$.
The integral of $\ln(x)$ can be found using integration by parts: $$\int \ln(x) \, dx = x \ln(x) - x + C$$.
Logarithmic functions are useful in solving integrals involving products of polynomials and exponentials.
Properties such as $\log_b(xy) = \log_b(x) + \log_b(y)$ and $\log_b(\frac{x}{y}) = \log_b(x) - \log_b(y)$ simplify complex expressions.
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Related terms
Exponential Function: A function of the form $f(x) = b^x$ where $b > 0$ and $b \neq 1$. It is the inverse function of a logarithmic function.