To determine how much more basic a solution with [tex]\( \text{pH} = 6 \)[/tex] is compared to a solution with [tex]\( \text{pH} = 3 \)[/tex], we need to understand the relationship between pH and hydrogen ion concentration.
The pH scale is logarithmic, which means each whole number on the scale represents a tenfold difference in hydrogen ion concentration. Specifically, a solution with a higher pH is more basic, and a difference of 1 pH unit corresponds to a tenfold decrease in the hydrogen ion concentration.
1. Calculate the difference in pH between the two solutions:
[tex]\[
\Delta \text{pH} = \text{pH}_{\text{higher}} - \text{pH}_{\text{lower}} = 6 - 3 = 3
\][/tex]
2. Given that the pH scale is logarithmic and each unit represents a tenfold change, a difference of 3 units equates to:
[tex]\[
10^{\Delta \text{pH}} = 10^3 = 1000
\][/tex]
Therefore, a solution with [tex]\( \text{pH} = 6 \)[/tex] is [tex]\( 1000 \)[/tex] times more basic than a solution with [tex]\( \text{pH} = 3 \)[/tex].
Based on the options provided, the correct answer is:
[tex]\[ 10^{\wedge} 3 = 1000X \][/tex]
