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

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 $e$ to base $10$:

$\log_{10} x = \paren {\log_{10} e} \paren {\ln x} = 0 \cdotp 43429 \, 44819 \, 03 \ldots \ln x$

Then $\log_{10} e = 0 \cdotp 43429 \ldots$ 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)