2. Aim: How do we solve exponential and logarithmic equations ? Do Now: Solve each equation: a. log 10 x 2 = 6 b. ln x = –3 Homework: Handout

3. Solve for x: 5 + 2 ln x = 4 2 ln x = –1 Combine like terms Isolate the log expression e ln x = e -1/2 Exponentiate both sides x = e -1/2 e ln is is equal to 1 x  0.607

4. Solve for x: 2 ln 3x = 4 ln 3x = 2 e ln 3x = e 2 3x = e 2 x  2.463

5. Solve for x: ln(x – 2) + ln(2x – 3) = 2 ln x ln[(x – 2)(2x – 3)] = ln x 2 ln(2x 2 – 7x + 6) = ln x 2 2x 2 – 7x + 6 = x 2 x 2 – 7x + 6 = 0(x – 1)(x – 6) = 0 x = 1, x = 6

6. Solve: e 2x – 3e x + 2 = 0 (e x ) 2 – 3e x + 2 = 0 treat the problem as a quadratic equation (e x – 2)(e x – 1) = 0 e x – 2 = 0, e x – 1 = 0 Factor Set each binomial equals to 0 e x = 2 e x = 1 ln e x = ln 2 x = ln 2, x = ln 1 ln e x = ln 1 x = 0.693, x = 0

7. Solve for x: a. 7 – 2e x = 5 b. 500e -x = 300 c. e 2x – 4e x – 5 = 0 d. 2 3 – x = 565 e.

8. Solve for x: 1. 2. 3.