PROPERTIES OF LOGARITHMS Section 7.5, Revised ©2013, vdang@houstonisd.org 5/2/2019 10:08 PM 7.5 - Properties of Logarithms

7.5 - Properties of Logarithms REVIEW EXPONENT RULES A. Product: B. Quotient: C. Power: n + m n – m n* m 5/2/2019 10:08 PM 7.5 - Properties of Logarithms

7.5 - Properties of Logarithms Logarithm PROPERTIES A. Product: B. Quotient: C. Power: + ÷ 5/2/2019 10:08 PM 7.5 - Properties of Logarithms

7.5 - Properties of Logarithms EXPAND VS CONDENSE A. Expanding Logarithms involves breaking down a simpler component into a complicated expression. The answer will involve more than one logarithm. B. Condensing Logarithms involves breaking down a complicated expression into simpler components. The answer will involve ONLY one logarithm. 5/2/2019 10:08 PM 7.5 - Properties of Logarithms

7.5 - Properties of Logarithms Example 1 Expand log3(4∙5) 5/2/2019 10:08 PM 7.5 - Properties of Logarithms

7.5 - Properties of Logarithms Example 2 Expand log 3x 5/2/2019 10:08 PM 7.5 - Properties of Logarithms

7.5 - Properties of Logarithms YOUR TURN Expand log4xy 5/2/2019 10:08 PM 7.5 - Properties of Logarithms

7.5 - Properties of Logarithms Example 3 Expand 5/2/2019 10:08 PM 7.5 - Properties of Logarithms

7.5 - Properties of Logarithms Example 4 Expand 5/2/2019 10:08 PM 7.5 - Properties of Logarithms

7.5 - Properties of Logarithms EXAMPLE 5 Expand 5/2/2019 10:08 PM 7.5 - Properties of Logarithms

7.5 - Properties of Logarithms YOUR TURN Expand 5/2/2019 10:08 PM 7.5 - Properties of Logarithms

7.5 - Properties of Logarithms Example 6 Condense log3x + log38 5/2/2019 10:08 PM 7.5 - Properties of Logarithms

7.5 - Properties of Logarithms Example 7 Condense log536 – log54 5/2/2019 10:08 PM 7.5 - Properties of Logarithms

7.5 - Properties of Logarithms YOUR TURN Condense and simplify, log26 – log24 5/2/2019 10:08 PM 7.5 - Properties of Logarithms

7.5 - Properties of Logarithms Example 8 Solve for x, log42 – log4x = log4(2/3) 5/2/2019 10:08 PM 7.5 - Properties of Logarithms

7.5 - Properties of Logarithms Example 9 Solve 5/2/2019 10:08 PM 7.5 - Properties of Logarithms

7.5 - Properties of Logarithms YOUR TURN Solve for x, log316 = xlog32 5/2/2019 10:08 PM 7.5 - Properties of Logarithms

7.5 - Properties of Logarithms Example 10 Condense and Simplify log5100 – 2log52 5/2/2019 10:08 PM 7.5 - Properties of Logarithms

7.5 - Properties of Logarithms Example 11 Condense (1/2)log536 –(1/3)log58 5/2/2019 10:08 PM 7.5 - Properties of Logarithms

7.5 - Properties of Logarithms YOUR TURN Condense (3log4x – 2log4y) + 7log4z 5/2/2019 10:08 PM 7.5 - Properties of Logarithms

7.5 - Properties of Logarithms Example 12 Using , approximate log 63 5/2/2019 10:08 PM 7.5 - Properties of Logarithms

7.5 - Properties of Logarithms Example 13 Using , approximate log 9/7 5/2/2019 10:08 PM 7.5 - Properties of Logarithms

7.5 - Properties of Logarithms Example 14 Using , approximate log 81 5/2/2019 10:08 PM 7.5 - Properties of Logarithms

7.5 - Properties of Logarithms YOUR TURN Using , approximate log 81/49 5/2/2019 10:08 PM 7.5 - Properties of Logarithms

7.5 - Properties of Logarithms Example 15 The Richter magnitude of an earthquake, M, is related to the energy released in ergs, E, by the formula . Find the energy released by an earthquake of magnitude 4.2. 5/2/2019 10:08 PM 7.5 - Properties of Logarithms

7.5 - Properties of Logarithms Example 15 The Richter magnitude of an earthquake, M, is related to the energy released in ergs, E, by the formula . Find the energy released by an earthquake of magnitude 4.2. 5/2/2019 10:08 PM 7.5 - Properties of Logarithms

7.5 - Properties of Logarithms Your turn The Richter magnitude of an earthquake, M, is related to the energy released in ergs, E, by the formula . Find the energy released by an earthquake of magnitude 6.2. 5/2/2019 10:08 PM 7.5 - Properties of Logarithms

7.5 - Properties of Logarithms ASSIGNMENT Worksheet 5/2/2019 10:08 PM 7.5 - Properties of Logarithms