Change of Base of Logarithm/Base 10 to Base 2

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:
 * $\lg x = \dfrac {\log_{10} x} {\log_{10} 2} = \dfrac {\log_{10} x} {0 \cdotp 30102 \, 99956 \, 63981 \, 19521 \, 37389 \ldots}$

Proof
From Change of Base of Logarithm:
 * $\log_a x = \dfrac {\log_b x} {\log_b a}$

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

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

can then be calculated or looked up.