Modulus of Change of Base of Logarithm/Examples/Base 10 to Base e

Example of Modulus of Change of Base of Logarithm

Let $\log_{10} x$ be the common (base $10$) logarithm of $x$.

Let $\log_e x$ be the natural (base $e$) logarithm of $x$.

Consider the change from base $10$ to base $e$:

$\ln x = \paren {\ln 10} \paren {\log_{10} x} = 2 \cdotp 30258 \, 50929 \, 94 \ldots \log_{10} x$

Then $\log_e 10 = 2 \cdotp 30258 \, 5 \ldots$ is the modulus.

Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): modulus (plural moduli)${}$: 2. (of logarithms)
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): modulus (plural moduli)${}$: 2. (of logarithms)