University:
Missouri State University
Course:
MTH 103 | Intermediate Algebra
Academic year:

2022
Views:

139

Pages:

9
Author:

Brent Cantu

TODAY'S AGENDA • Return Quizzes Warm Up Check HW Lesson: Solving Exponentials Unit 3 Test: Wednesday! GOAL WHEN SOLVING LOG EQUATIONS: Use properties of logs to get equation into logbx=logy and use one to one property If equation has a log (or In) on only one side, then change to exponetial form and evaluate SOLVING LOGS HOMEWORK 1. x = 7 8. x=4 15. No Sol. 2. x = 2 9. x = 1 16. x = 5 3. x = 11 10. x = 5 4. x = 2 11. x=4 Application 5. x=4 12. x = 5 a) 79.5 6. x = 9 13. No Sol b) 73.3 7. x = 9 14. x = plus/minus sqrt(7) c) 6 months ANSWER KEY ) log_2(2x - 3) = log_2(x + 4) 2x - 3 = x + 4 x = 7 3) 2 * log(x) = log(x) * 121 log_7((x ^ 2) / i * c*g_{7}) 1 partial1 x ^ 2 = 121 x = pm i 11 x = 11 *con NOT log a negative nureber 5) log_3(6) + log_(3X)(log_3(7)) = log_3(168) log_3(42x) = log_3(168) 4ax = 168 x = 4 2) 2 * log_4(8x) = 4 log_4(8x) = 2 4 ^ 2 * r I_{G} = 0.8x 4) Jogex-log(x-1) I_{4} * x/(x - 1) = 1/2 log 4 4 ^ 2 = x/(x - 1) a = x/(x - 1) a(x + 0) = x 6)3-5 logsx x = 2 i * log_3(x) = - 10 log_3(x) = 2 3 ^ 2 = x x = 7) log_3(x) + log_3(x - 8) = 2 log 3 * (x - 8) = 2 3 ^ 2 = x ^ 2 - 8x 0 = x ^ 2 - 8x - 9 0 = (x - 9)(x + 1) x = 9x - 4 x = 9 9) log_3(5x + 13) - log_3(6) = log_3(3x) log_3((5x + 13)/6) = log_s(3x) x = 1 (5x + 13)/6 = 3x 5x + 13 = 18x 13 = 13x 8) log_6(3x + 28) - log_6(5) = log_6(2x) log_6((3x + 28)/5) = log_6(2x) (3x + 78)/5 = 2x 3x + 28 = 10 * x 28 = 7x x ^ 2 * 4 10) log_4(x - 3) + log_4(x + 3) = 2 log_4(x - 3) * (x + 3) = 2 4 ^ 2 = x ^ 2 - 9 16 = x ^ 2 - 9 25 = x ^ 2 x =X5 x = 5 11) 1/2 * ln(x) = ln(2) ln(sqrt(x)) = ln(2) sqrt(x) = 2 x = 4 13) log_a(x - 1) = log_a(x - 2) - log_x(x + 2) log_8(x - 1) = log_8((x - 3)/(x + 2)) x - 1 = (x - 3)/(x + 2) (x - 1)(x + 2) = X - 2 x ^ 2 + x - 2 = x - 2 x ^ 2 = 0 x = 6 12) 2/3 * log(48) + log(4X) = 1/2 * (log(416) + log(425)) log_4(root(8, 1) ^ 2) + log_4(x) = plus/minus log_4(400) log_4(4x) = log_4(sqrt(400)) 4x = 20 x = 5 14) In x ^ 2 - ln(7) = 0 ln(x ^ 2) * ln(7) x ^ 2 = 7 x = plus/minus sqrt(7) 15) n(x+\$)= ln(x - 1) - ln(x + 1) . In r(x + 5) = ln((x - 1)/(x + 1)) x + 5 = (x - 1)/(x + 1) Ø (x + 5)(x + 1) = x - 1 x ^ 2 + 6x + 5 = x - 1 x ^ 2 + 5x + 6 = 0 x > - 3 x + 2 ( x + 3y(x + 2) = 0 ApplicationModel Students were tested momhly to denarmine how much larned material they rataimed. The average scores for the group can be modeled by the human memory model f(0 - 90 - 15) (113, 05≤12 where 1 in the time in month a) Wat was the average score after 4 months? (sundial decimal) 90 - 15 * log(4 + 1) * boxed 79.5 10 What was the degunal) 90 - 15 * log(12 + 1) = boxed 133 e) Determine when 77.32 7.32 = 90 - 15 * log(t + 1) 868 = - 15 * log(t + 1) 0.845 = log(4.1) 10^ *245 = t + 1 72++1 t= G months Warm Up.... WOULD YOU RATHER...... Have 35 min of homework each night for the rest of the semster (50 days) OR have 1 second tonight and it doubles each of the following nights????? DO YOUR 5 16) log(x + 3) + log(x - 3) = 2 * log(4) log(x ^ 2 - 9) = log(4 ^ 2) x ^ 2 * 9 = 16 x ^ 2 = 25 X=5 x = 5