When the hydronium ion concentration of a solution is increased by a factor of 10, it means that

The pH of the solution will decrease by 1 unit.

Explanation:

Let say the hydronium ion concentration of a solution is 0.001

pH = - log [H+]

= -log 1.0 x 10^3 = 3

if the hydronium ion concentration is increased by 10 , that is: 0.001 x 10 = 0.01

pH = -log [1.0 x 10^2]

= 2

Therefore, the pH is reduced by 1 unit when the hydronium ion concentration is increased by a factor of 10.