Change of Base of Logarithm/Base 10 to Base e

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

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

Then:
 * $\log_e x = \log_e 10 \log_{10} x = 2.30258\ 50929\ 94 \ldots \log_{10} x$

Proof
From Change of Base of Logarithm:
 * $\log_a x = \log_a b \ \log_b x$

Substituting $a = e$ and $b = 10$ gives:
 * $\log_e x = \log_e 10 \log_{10} x$

The value:
 * $\log_e 10 = 2.30258\ 50929\ 94 \ldots$

can be calculated or looked up.