Common Logarithm of Number in Scientific Notation

Theorem
Let $n$ be a positive real number which is presented (possibly approximated) in scientific notation as:


 * $n = a \times 10^d$

where:
 * $1 \le a < 10$
 * $d \in \Z$ is an integer.

Then:


 * $\log_{10} n = \log_{10} a + d$

where:
 * $0 \le \log_{10} a < 1$

Proof
We are given that:
 * $1 \le a < 10$

It follows from Range of Common Logarithm of Number between 1 and 10 that:
 * $0 \le \log_{10} a < 1$