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# Class Note for MATH 1310 at UH

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This 7 page Class Notes was uploaded by an elite notetaker on Friday February 6, 2015. The Class Notes belongs to a course at University of Houston taught by a professor in Fall. Since its upload, it has received 17 views.

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Date Created: 02/06/15

The Product and Quotient Rule Let b M and N be positive real numbers and b not equal to 1 log b MN 2 log b M log b N Product Rule 10gb 2 10gb M log N Quotient Rule The Power Rule Let b andM be positive real numbers and b not equal to l and let 1 be any real number long 1110ng Properties of Logarithms For b gt 0 and b not equal to 1 and real numbers Mgt 0 Ngt 0 and n 10gbb1 10gb 1 O The Product Rule Change of Base Formula 10gb MN log M 10gb N 10gb M loga M The Quotient Rule loga b logb logbltMgt IogbltNgt l 10gb j 10gbN The Power Rule 10gb M 1410ng Inverse Properties of Logarithms 191 ng 2 M 10gb 9M 2 M Example 1 Expand the following logarithmic expression Your answer should not contain logarithms of any product quotient or power loglOOOABZ Example 2 Expand the following logarithmic expression Your answer should not contain logarithms of any product quotient or power l l 10g4 y12 Example 3 Expand the following logarithmic expression Your answer should not contain logarithms of any product quotient or power In e x l x2 16 Example 4 Rewrite the following expression as a single logarithm l ZlogxZlogy Example 5 Rewrite the following expression as a single logarithm logx 3logy logz 2 510gw l Example 6 Rewrite the following expression as a single logarithm logsw2 l 8log5 x 3log5x l210g5 x Example 7 Evaluate the following using the laws of logarithms Simplify your answer as much as possible without using a calculator 104log3 Example 8 Evaluate the following using the laws of logarithms Simplify your answer as much as possible without using a calculator log6 10 log6 36 Example 9 Evaluate the following using the laws of logarithms Simplify your answer as much as possible without using a calculator log2 36 log2 9 The Change of Base Formula For any logarithmic bases at and b and any positive number M loga M 10 M 2 gb loga b Example 10 Use the Change of Base Formula to write the following in terms of natural logarithms Then use a calculator to write your answer as a decimal correct to the nearest thousandth 10g5 8 Example 11 Use the Change of Base Formula to write the following in terms of natural logarithms Then use a calculator to write your answer as a decimal correct to the nearest thousandth 10g9 31 Math 1310 Chapter 5 Section 54 Properties of Logarithms

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