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Hello, I was given this math question in class last week, but I was never able to figure it out. I am not bad with exponential growth/decay, but this one is tricking me up. Can you help me, I am having a tough time getting through this problem.

The question, from my Pre-Calculus & Trigonometry class is:
The Chemical acidity of a solution is measured in units of pH: pH = -log[H^+], where [H^+] is the hydrogen ion concentration in the solution. If a sample of rain has a pH of 3.2, how many times higher is its [H^+] than pure water's, which has a pH of 7?

This is a math-class question, so it shouldn't require a ton of science background. Any and all help is appreciated.

Answer
Since pH is the negative of the log (base 10) of the concentration [H^+], it follows that

[H^+]  = 10^(-pH)

which is just the inverse. So taking the 2 pH values and inverting them we get

[H^+]1 = 10^[-3.2] = 6.3x10^-4  and  [H^+]2 = 10^[-7], so that

[H^+]1 / [H^+]2 = 6.3x10^3

or a little over 6000 times larger.

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randy patton

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college mathematics, applied math, advanced calculus, complex analysis, linear and abstract algebra, probability theory, signal processing, undergraduate physics, physical oceanography

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26 years as a professional scientist conducting academic quality research on mostly classified projects involving math/physics modeling and simulation, data analysis and signal processing, instrument development; often ocean related

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J. Physical Oceanography, 1984 "A Numerical Model for Low-Frequency Equatorial Dynamics", with M. Cane

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