A logarathim question:

pH = – log h

The pH of a solution is dependent on the concentration of hydronium ions, h, and can be calculated by the equation above. If the concentration of hydronium in solution A is 100 times the concentration of the hydronium in solution B, what is the absolute value of the difference in their pH values?

A. –2

B. 2

C. 3

D. 10

E. 100

Hmm…Is this ACT? Subject Test? Definitely not SAT with logs (not to mention 5 answer choices). No matter—I got you.

Easiest way to go here is just to plug in a couple values for the concentrations of solutions A and B. Let’s say A has a concentration of 1,000,000 and B has a concentration of 10,000. That meets the requirement of the question: the concentration of A is 100 times more than the concentration of B. Now just calculate both pH values (using log base 10 in case that’s not your calculator’s default):

And there you have your answer—the pH values are 2 apart. Don’t be fooled by choice A: the question asks for the absolute value of the difference so you definitely don’t want a negative number.

Thanks, Mike! Yes, it appears to be from the ACT. Thanks for the great explanation, as always – despite being off-topic for the SAT!