Approximation to Binary Logarithm from Natural and Common Logarithm

Theorem
The binary logarithm $\lg x$ can be approximated, to within $1 \%$, hy the expression:
 * $\lg x \approx \ln x + \log_{10} x$

That is, by the sum of the natural logarithm and common logarithm.

Proof
We have that:
 * $\ln 2 = 0 \cdotp 69347 \ 1805 \ldots$
 * $\log_{10} e = 0 \cdotp 43429 \ 44819 \ldots$

Thus:

Hence:
 * $\lg x + \log_{10} x \approx 0 \cdotp 994 \ln x$

That is, the approximation is $99.4 \%$ accurate.