7.5a - Properties of Logarithms

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Presentation transcript:

7.5a - Properties of Logarithms Worksheet Key 12/7/2018 8:28 PM 7.5a - Properties of Logarithms

7.5a - Properties of Logarithms Worksheet Key 12/7/2018 8:28 PM 7.5a - Properties of Logarithms

7.5a - Properties of Logarithms Worksheet Key 12/7/2018 8:28 PM 7.5a - Properties of Logarithms

7.5a - Properties of Logarithms Worksheet Key 12/7/2018 8:28 PM 7.5a - Properties of Logarithms

7.5a - Properties of Logarithms 12/7/2018 8:28 PM 7.5a - Properties of Logarithms

Section 7.5A, Revised ©2013, vdang@houstonisd.org NATURAL LOGARITHMS Section 7.5A, Revised ©2013, vdang@houstonisd.org 12/7/2018 8:28 PM 7.5a - Properties of Logarithms

7.5a - Properties of Logarithms Conversions The base of Natural Log (ln) is e. Convert: lne x = y to ey = x 12/7/2018 8:28 PM 7.5a - Properties of Logarithms

7.5a - Properties of Logarithms Example 1 Convert ln 2/5 = –0.916 to exponential form 12/7/2018 8:28 PM 7.5a - Properties of Logarithms

7.5a - Properties of Logarithms Your Turn Convert ln 679 = 6.520 to exponential form 12/7/2018 8:28 PM 7.5a - Properties of Logarithms

7.5a - Properties of Logarithms Example 2 Convert e2 = 7.389 to logarithmic form 12/7/2018 8:28 PM 7.5a - Properties of Logarithms

7.5a - Properties of Logarithms Your Turn Convert e2x = 3 to logarithmic form 12/7/2018 8:28 PM 7.5a - Properties of Logarithms

Simplifying Natural Logarithms The inverse of a natural base (e) is the natural log (ln) If there is ln and e, they cancel each other out Natural logarithms have the same properties as log base 10 and logarithms with other bases The base of a natural log is e but it will never be written as the base. ln + e = FELONY 12/7/2018 8:28 PM 7.5a - Properties of Logarithms

Natural Logarithm Steps ISOLATE the x CONVERT by incorporating e as the base to both sides Cancel any ln e ’s Simplify using Natural Logarithm rules Check 12/7/2018 8:28 PM 7.5a - Properties of Logarithms

7.5a - Properties of Logarithms Example 3 Solve ln x = 4 12/7/2018 8:28 PM 7.5a - Properties of Logarithms

7.5a - Properties of Logarithms Example 4 Solve 5 + 2 ln x = 7 12/7/2018 8:28 PM 7.5a - Properties of Logarithms

7.5a - Properties of Logarithms Your Turn Solve 3 ln x – 6 = 9 12/7/2018 8:28 PM 7.5a - Properties of Logarithms

Natural Logarithm Rules Product: Quotient: Power: 12/7/2018 8:28 PM 7.5a - Properties of Logarithms

7.5a - Properties of Logarithms Example 5 Expand ln 3x4 12/7/2018 8:28 PM 7.5a - Properties of Logarithms

7.5a - Properties of Logarithms Your Turn Condense (ln 4 + 3 ln 3) – ln 12 12/7/2018 8:28 PM 7.5a - Properties of Logarithms

7.5a - Properties of Logarithms Example 6 Solve ex + 5 = 60 12/7/2018 8:28 PM 7.5a - Properties of Logarithms

7.5a - Properties of Logarithms Example 7 Solve –14 + 3ex = 11 12/7/2018 8:28 PM 7.5a - Properties of Logarithms

7.5a - Properties of Logarithms Your Turn Solve 7 – 2ex = 5 12/7/2018 8:28 PM 7.5a - Properties of Logarithms

7.5a - Properties of Logarithms Review Solve x2 – 3x + 2 = 0 12/7/2018 8:28 PM 7.5a - Properties of Logarithms

7.5a - Properties of Logarithms Example 8 Solve e2x – 3ex + 2 = 0 12/7/2018 8:28 PM 7.5a - Properties of Logarithms

7.5a - Properties of Logarithms Example 8 Solve e2x – 3ex + 2 = 0 12/7/2018 8:28 PM 7.5a - Properties of Logarithms

7.5a - Properties of Logarithms Example 9 Solve e2x – 7ex + 12 = 0 12/7/2018 8:28 PM 7.5a - Properties of Logarithms

7.5a - Properties of Logarithms Example 10 Solve 2e2x + 7ex – 4 = 0 12/7/2018 8:28 PM 7.5a - Properties of Logarithms

7.5a - Properties of Logarithms Your Turn Solve 6e2x + 11ex – 2 = 0 12/7/2018 8:28 PM 7.5a - Properties of Logarithms

7.5a - Properties of Logarithms Assignment Worksheet 12/7/2018 8:28 PM 7.5a - Properties of Logarithms