Final answer:
Compared to a solution with a pH = 10, a solution with pH = 13 is 1000 times more basic, as the pH scale is logarithmic with each unit indicating a tenfold change in hydrogen ion concentration.
Step-by-step explanation:
Compared to a solution with a pH = 10, a solution with pH = 13 is 1000X more basic. The pH scale is logarithmic, meaning a change in pH of 1 unit reflects a tenfold change in hydrogen ion concentration.
A solution with a higher pH is more basic, and because each unit on the pH scale corresponds to a tenfold difference in [H+] concentration, a difference of 3 pH units (from pH 10 to pH 13) means the [H+] concentration is 10 x 10 x 10 (or 1000) times less. Thus, the pH 13 solution is 1000 times more basic than the pH 10 solution.