Change of Base of Logarithm/Base 2 to Base 10

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

Let $\lg x$ be the binary (base $2$) logarithm of $x$.

Then:
 * $\log_{10} x = \left({\lg x}\right) \left({\log_{10} 2}\right) = 0 \cdotp 30102 \, 99956 \, 63981 \, 19521 \, 37389 \ldots \lg x$

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

Substituting $a = 10$ and $b = e$ gives:
 * $\log_{10} x = \left({\lg x}\right) \left({\log_{10} 2}\right)$

The common logarithm of $2$:
 * $\log_{10} 2 = 0 \cdotp 30102 \, 99956 \, 63981 \, 19521 \, 37389 \ldots$

can be calculated or looked up.