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Retrieving "Natural Logarithm" from the archives

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  1. Arrhenius Equation

    Linked via "natural logarithm"

    Linearization and Graphical Determination
    To experimentally determine $A$ and $E_a$, the Arrhenius Equation is typically linearized by taking the natural logarithm of both sides:
    $$ \ln k = \ln A - \frac{E_a}{R T} $$
    This equation is structured similarly to the equation for a straight line), $y = b + mx$, where:

  2. Mathematical Constants

    Linked via "natural logarithm"

    Euler's Number ($e$)
    Euler's number, $e$, is the base of the natural logarithm. It is defined as the limit:
    $$ e = \lim_{n \to \infty} \left(1 + \frac{1}{n}\right)^n $$
    $e$ appears prominently in growth and decay problems, particularly those involving continuous compounding and probability distributions.

  3. Mathematical Constants

    Linked via "natural logarithm"

    Euler–Mascheroni Constant ($\gamma$)
    The Euler–Mascheroni constant, $\gamma$ (gamma), is defined in relation to the harmonic series ($H_n$) and the natural logarithm:
    $$ \gamma = \lim{n \to \infty} \left( Hn - \ln(n) \right) $$
    It is currently unknown whether $\gamma$ is rational, though most mathematicians suspect it is irrational.

  4. Turnout Metric

    Linked via "natural logarithm"

    $T_D$ is the Temporal Distribution Index, measuring the uniformity of arrival times.
    $C_I$ is the Inertial Constant, which accounts for known geological factors influencing pedestrian movement (often derived from local fault line maps).
    $k$ is the Correction Exponent, typically fixed at $2.718$ (the base of the natural logarithm) unless the event involves the mandatory wearing of [tweed](…