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\Huge{
Logarithms in Practice}{\small{take 2}}
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\noindent \emph{pH Scales:} Let $[H^+]$ be the concentration of hydrogen ions in solution $X$ measured in moles per liter (denoted $M$).  Then 

$$\text{pH level of solution }X=-\log [H^+]$$

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\begin{enumerate}

\item What is the pH level of human blood if the concentration of hydrogen ions in blood is about $3.16*10^{-8}$M?
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\item What is the pH level of battery acid if the concentration of hydrogen ions in battery acid is about $0.1$M?
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\item What is the $[H^+]$ of stomach acid if the pH value of stomach acid is 2.3?
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\item How many more times concentrated is the battery acid $[H^+]$ to vinegar's concentration where vinegar commonly has a pH value of 3?


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\noindent \emph{Richter Scale:} Let $I$ be the intensity of an earthquake $X$ and $S$ be the intensity of a `standard' earthquake.   Then the measurement of an earthquake $X$ as measured on the Richter Scale is: 

$$\log \left(\frac{I}{S}\right)$$

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\item In March of 2011 Japan's earthquake was 9.0 on the Richter Scale.  February 2001 Tacoma had an earthquake measuring 6.8 on the Richter Scale.  How many more times more intense was Japan's earthquake to the one in Tacoma?
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\noindent \emph{Decibels:} The loudness of a sound is measured in decibels and is related to the intensity $I$ by

$$10\log \left(\frac{I}{S}\right)$$

\noindent where $S=10^{-12}$ W/m$^2$ 
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\item France passed a law limiting iPods and other MP3 players to a maximum possible volume of 100 decibels.  Find the maximum intensity (in W/$\text{m}^2$) an iPod is legally allowed to output in France.   
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\item Normal conversation has a sound level of about 65 decibels. How many more times intense than normal conversation is the sound an iPod operating at the French maximum of 100 decibels?
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