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 $x$.

Then:
 * $\log_{10} x = \log_{10} e \log_e x = 0.43429\ 44819\ 03 \ldots \log_e x$

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

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

The value:
 * $\log_{10} e = 0.43429\ 44819\ 03 \ldots$

can be calculated or looked up.