Change of Base of Logarithm/Base e to Base 10

Theorem

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

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

Form 1

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

Form 2

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