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<p>Thedecibel(dB) is the unit to measure the intensity of a sound. It is alogarithmic unitused to express the ratio between two values of a physical quantity. The smallest audible sound (near total silence) is 0 dB. A sound 10 times more powerful is 10 dB. A sound 100 times more powerful (102) is 20 dB.</p>
<p>In other words, when you increase sound (in terms of decibels) it is an exponential increase.How Loud is Too Loud Activity</p>
<p>Audible wavelengths vary from animal to animal</p>
<p>Properties of LogarithmsWhat is a Logarithm?A quantity representing the power to which a fixed number (the base) must be raised to produce a given numberWhat is it used for?Multiplying large numbers without the use of a calculatorRemember calculators were not readily available to the masses until about 50 years ago. Weve come a LONG way since then in technology.</p>
<p>GreekGreekModern LatinLogosReckoning,Ratio</p>
<p>ArithmosnumberOriginlogarithmusLogarithm(log)Early 17th centuryWhy do we need Logarithms?Calculators have advanced enough that even the most basic of calculators can easily compute logarithms for us, however, its important that we still understand the use of logarithms.</p>
<p>The exponential function y=ax is one of the most important functions in mathematics, physics, and engineering. Radioactive decay, bacterial growth, population growth, continuous interest, etc. are all exponential examples we use everyday.</p>
<p>How do you solve for x if it is in the exponent? (y=ax)</p>
<p>We need logarithms to help us solve.</p>
<p>y = ax is equivalent to loga(y) = xExamplesWrite the following in logarithmic/exponential form:ExamplesEvaluate the expressionDifferent Bases:(We will practice logarithms using a variety of different bases.)Below you will find a list of the most common forms.Base 10 is used by chemists in their measurements of pH, the acidity of a liquid. We often call this the common base.</p>
<p>Base 2 is used in information theory and computers (used in transmitting information and measuring the errors made and how to correct those errors).</p>
<p>Base e, where e=2.718281828..., is used in calculus and is probably the most important base.Lets Discover the Properties of LogarithmsHeres what you should have come up withHeres what you should have come up withORHeres a few others for your notesStart with the exponent law of logarithmsUse the division/subtraction law of logarithmsSimplifyNote: We DID NOT DIVIDE BY LOG! This is not a defined mathematical principle.We concluded that both sides of the equation had log10 therefore their values are equivalent.Lets look at some real applications...Decibels</p>
<p>Earthquakes</p>