Lesson 5.4: Exponential & Logarithmic Equations 2 Basic - PowerPoint PPT Presentation

Lesson 5.4: Exponential & Logarithmic Equations 2 Basic strategies for solving Exponential and Logarithmic equations:   x y a a iff x y 1.Use 1-to-1 properties:   log x log y iff x y a a  log a x 2. Use Inverse properties: a x  x log a x a

Ex 1: Solve for x. Using 1-1 properties b. ln x – ln 3 = 0 a.2 x = 32 x  2 5 2 x  ln ln 3 x  3 x  5 F H I 1 x   1 x  x 3 2 9 3 K  9 c. 3 3   x 2 x   2

Ex 1: Solve for x. Using Inverse properties d. e x = 7 e. ln x = -3 ln  e x   3 x ln ln 7 e e   3  .050 x ln e ln 7  x e x  ln7  1946 . f. log 10 x = -1 10 1  1 x   x   log 1 10 10 10 10

Recap of Strategies Used: 1.Rewrite original equation in a form that allows the use of 1-to-1properties. 2.Rewrite an exponential equation in logarithmic form and apply Inverse properties. 3.Rewrite a logarithmic equation in exponential form and apply Inverse properties.

Ex 2: Solve for x. Exponential Equations a. 4 x = 72 b. 3(2) x = 42 x  3 3 log 4 log 72 x  4 4 2 14 x  log 72 10 x  log 2 log 14 log 4 2 2 10 x  log 14 10  3085 . log 2 10  3807 .

Ex 2: Solve for x. c. e x + 5 = 60 e x  55 e x  ln ln 55 x  ln55  4 007 .

Ex 2: Solve for x. Logarithmic Equations e. log 3 (5x – 1) = log 3 (x + 7) d. ln x = 2 ln    log x log y iff x y x 2 e e a a    5 x 1 x 7  2 x e  1  1    7389 . 5 x x 8  x  x x  2 x  4 8

Ex 2: Solve for x.  1 ln  f. 5 + 2 ln x = 4 x  5  5 e e 2  1 ln x   2 1  x e 2 2 2  0 607 . ln x   1 2 Homework: p.403 #9-20 all