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Solve for x (hint: first, convert each from logarithmic to exponential form) a) log9 x = 1 Answer: x = 9 b) loga x = 1 Answer: x = a c) ln x = 1 Answer: x = e (why?) 4. Solve for x (hint: first, convert each from logarithmic to exponential form) a) log9 x = 0 Answer: x = 1 b) logx x = 0 Answer: x = 1 c) ln x = 0 Answer: x = 1 (why?) loga a = 1 ; loge e = 1 or ln e = 1loga1 = 0 ; loge1= 0 or ln 1 = 0 Properties of logarithms RuleFormulaExampleI) Multiplicationln (AB) = ln A + ln Bln 5x = ln 5 + ln xII) Division EMBED Equation.3 ln 5 / x = ln 5 - ln xIII) Power EMBED Equation.3 ln5x = x ln 5 Examples: Example 1 : Express in term of logarithms: a) log (x2y2) b) log EMBED Equation.3  c) log EMBED Equation.3  Example 2: Express as a single logarithm: a) 3 ln x + 4 ln y - 3 ln z b) 2 log x - 3 log y + 2 log z Example 3: (to be solved and finished in class) Solve for x: a) 5x = 10 b) ln x = 4 c) 3x = 5 d) log3 (2x- 1) - log3 (x- 4) = 2 e) log3 (x - 4) + log3 (x+ 4) = 3 f) log x + log (x - 3) = 1 g) log2x + log2(x - 2) = 3 Example 4: (to be solved in class, but finished at home) Solve for x: a) ln x = -2 b) log2x + log2(x 2) = 3 c)  EMBED Equation.3  d) log4(x + 6) - log4x = 2 e) ln(2t + 1) + ln (2t 1) = 0 f) ln(t - 1) = 3 g) EMBED Equation.3  h)  EMBED Equation.3  i)  EMBED Equation.3  Answers (not on order): (2/5) ; (4) ; (1/e2) ; (e3+ 1) ; ( 0 , -1) ; ( EMBED Equation.3 ) ; (3+ln 0.8) ; (0.3466) ; (2.322) Homework To Be Turned In: Solve for t using natural logarithms: 1) et = 100 2) et = 60 3) e-0.02t = 0.06 4) ln t =2 5) ln t = -3 6) e 0.07t = 2 7) 2t = 43 8) 4t = 8 9) 6t = 10 10) (5.2)t = 70 11)  EMBED Equation.3  12) EMBED Equation.3  13)  EMBED Equation.3  14)  EMBED Equation.3  15)  EMBED Equation.3  16)  EMBED Equation.3  17)  EMBED Equation.3  18)  EMBED Equation.3  Answers (not on order): (141) , (9.9021) , (1.2851) , (1.3863) , ( 0.47) , (4.6) , (2.5769) , (4.1) , (1.5) , (5.4263) , ( 0 ) , (e2) , (e-3) , (0.55) , (0.314) , ( EMBED Equation.3 ) , (8.39) , ( 2 ) PAGE 1 PAGE 2  6ABUVWYlmno|}.?\abuvwy뿺뿺ߨ랕ߌjCJEHUjCJEHUj > UVmHjCJEHU5CJCJEHCJEH6CJjhCJEHUj > UVmHjCJEHUj: CJUVmHCJ jCJU 5>*CJ5CJ7@Apq`a"?`,K:Y~$$@Apq`a"?`,K:Y~ 7 : f % < = H ` n o p { | þ#$%  3  K  VW  n                 :   '(.59:CDGMTXYdefhimtxyz345<CEFGRST[begijl 6CJEHCJCJEH 6CJEH 6CJEHCJEH6CJCJ jCJUjCJEHUj > UVmHK"#$%,345ABCDKRSTWY`ahopqtu}~     ! 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