Range of Common Logarithm of Number between 1 and 10

Theorem
Let $x \in \R$ be a real number such that:
 * $1 \le x < 10$

Then:
 * $0 \le \log_{10} x \le 1$

where $\log_{10}$ denotes the common logarithm function.

Proof
We have:

The result follows from Logarithm is Strictly Increasing.