University:
High School
Course:
High School Algebra
Academic year:

2023
Views:

117

Pages:

3
Author:

engranaje085z

A2 4.20 - 4.24 Notes April Section 6-5: Properties of Logarithms Target 68 We are learning the properties of logarithms so that we can solve logarithmic equations. 3 Properties are used to expand & condense logarithms: 1 1. Expand the logarithmic expressions: log₆ 3x⁴ = log₆ 3 + log₆ x⁴ = log₆ 3 + 4log₆ x ln 5/12x = ln 5 - ln 12x = ln 5 - (ln 12 + ln x) = ln 5 - ln 12 - ln x log₇ √4 = log₇ x^(1/4) = 1/4 log₇ x Product Property logb m + logb n = logb mn Quotient Property logb m - logb n = logb (m/n) Power Property logb m^n = n logb m These properties are similar to exponents. Condense the logarithmic expressions: log₂ 5 + log₂ 4 = log₂ (5 * 4) = log₂ 20 3log₅ x + log₅ 7 = log₅ x³ + log₅ 7 = log₅ 7x³ 2log x - log 9 = log x² - log 9 = log (x²/9) ln x + 3ln y - ln 12 = ln x + ln y³ - ln 12 = ln (x * y³) - ln 12 = ln (xy³/12) A2 4.20 - 4.24 Practice (Properties of Logarithms) Expand each logarithmic expression. log x⁶ = 6 log x log 4x³ = log 4 + log x³ = log 4 + 3 log x log (x - y) ln (2/x²) = ln 2 - ln x² = ln 2 - 2 ln x log √3 = log u^(1/3) = 1/3 log u log₅ √3x = log₅ (3x)^(1/2) = 1/2 log₅ 3x = 1/2 (log₅ 3 + log₅ x) log₄ 2√x = log₄ 2 + log₄ x^(1/2) = log₄ 2 + 1/2 log₄ x Condense each logarithmic expression. 6 log₆ x + 3 log₆ y = log₆ x⁶ + log₆ y³ = log₆ x⁶y³ ln a + ln b + 2 ln c = ln a + ln b + ln c² = ln abc² log 50 - log 2 = log (50/2) = log 25 5 log₇ u + 25 log₇ v = log₇ u⁵ + log₇ v²⁵ = log₇ u⁵v²⁵ Challenge: 3 log₇ z + 1/2 log₇ x = log₇ z³ + log₇ x^(1/2) = log₇ z³ * x^(1/2) = log₇ z³√x