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Unformatted text preview: Lesson_8.7_SolvingExpLogProbs.notebook 8.7 Solving Problems with Exponential and Logarithmic Functions
When a range of values can vary greatly, using a logarithmic scale with powers of 10 makes comparisons between the large and small values more manageable. Some examples of logarithmic scales are: (1) the pH scale (2) the Richter scale
(3) the decibel scale To compare concentrations on the pH scale, intensity on the Richter scale, or sound intensities, determine the quotient between the values being compared. Example #1:
The intensity of one sound can be compared to that of another sound of the same frequency by taking the ratio of their exponents: where I0 is the minimum intensity detectable by the human ear, I is the intensity of the sound being measured, and L is the loudness measured in decibels (dB). (a) A busy street has a loudness of 70 dB. How many times more intense is the street noise compared to the minimum detectable level? Lesson_8.7_SolvingExpLogProbs.notebook (b) A normal conversation has a loudness of 60 dB. How many times more intense than a normal conversation is shouting, which has a loudness of 80 dB? (Now do you understand why I always ask you to keep your voices down? J) Example #2: The Richter scale was introduced by American seismologist Charles F. Richter in 1935 to measure the magnitude of earthquakes. The magnitude of an earthquake of intensity, I, measured on the Richter scale is given by the following equation, where I0 is the minimum measure of a reference earthquake. An earthquake with a measure of x on the Richter scale has a true intensity of 10x. (a) If an earthquake has an intensity that is 107.8, what is its magnitude on the Richter scale? Lesson_8.7_SolvingExpLogProbs.notebook (b) How many times more intense was an earthquake that measured 7.5 on the Richter scale than an earthquake that measured 6.2? Example #3: In chemistry, the pH of a solution is a measure of its acidity. The pH value is defined by pH = log[H+], where [H+] is the Hydrogen ion concentration in moles per litre (mol/L). (a) Find the pH for tomatoes if the hydrogen ion concentration, [H+], is 6.3 x 105 mol/L. Lesson_8.7_SolvingExpLogProbs.notebook Example #3 (continued): In chemistry, the pH of a solution is a measure of its acidity. The pH value is defined by pH = log[H+], where [H+] is the Hydrogen ion concentration in moles per litre (mol/L). (b) If the pH of sea water is 8.5, find the hydrogen ion concentration. Example #3 (continued): In chemistry, the pH of a solution is a measure of its acidity. The pH value is defined by pH = log[H+], where [H+] is the Hydrogen ion concentration in moles per litre (mol/L). (c) How much stronger is an acid with a pH 1.9 than an acid with pH 3.8? Homework
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