1. Lesson 13 solving for x in log problems January 29, 2014

2. Lesson 13 1. Use the product rule to rewrite this expression. log 2t + log x 2. Rewrite each expression in log form, then solve 2 x = 5 3. Determine if this statement is t/f if false rewrite log 3 - log 5 = log 15 4. Write the inverse of the following function. f(x) = ¼ x + 5 5. Sketch the following function and its inverse. y = 2x 2

3. Review Lesson 12 1a. g h  g k b. log stc. f w-v d. log h – log k 2a. 1.25b. 1.85c. 3.1d. 1259 e. 1349f. 3.1g. varyingh. log ab 3. a. log 3 28 = x = 3.03b. log 5 14 = x = 1.64 c. log 2.128 = x = -2.97d. log 8 1982 = x= 3.65 e. log 2 129 = x = 7.01f. log 5.0123 = x = -2.73 g. log 6 123.36 = x = 2.69h. log 7 10 = x = 1.18 4a trueb. false; = log 15 c. false; 4 log 2 or 2 log 4 c. Truee. false; = log 3 f. false; log 7 + log 5

4. Lesson 13 b 1. Y = 75(3) x 2. 4 6 /7 15 3. 2y 2 /3x4. 4y 5 /x 13 5. 7/36. -17. f(x) = 729(1-.13) x 8. -4, - 20 / 3, - 100 / 9, - 500 / 27, - 2500 / 81 9. .46 10. About 4 years11. $21,399.66

5. Solving for x as an exponent Notes x = log 3 24 Apply the logarithmic change of base property x = Log 24 Log 3 Type in log (24) / log (3 x =2.89

6. Lesson 13 practice Solve for x x = log 9 24x = log 5 32 x = log 6.24 x = log 7 1x = log 3 3 x = log 3 9 1.452.15-0.80 012 1. 2. 3. 4. 5. 6.

7. Notes Solving for x as a base 4 = log x 24 Put in exponent formx 4 = 24 Raise to the power of the reciprocal exponent (x 4 ) 1/4 = (24) 1/4 Type the number (24) ^ then ( then “the reciprocal exponent”, then ) x = 2.21

8. Practice Lesson 13 Solve for x 3 = log x 212 -2 = log x.0215 1 = log x 5 2 = log x 36 5 = log x 32 3 = log x 125 5.96 6.82 5 6 5 2 7. 8. 9. 10. 11. 12.

9. Notes Solving for x when its the argument 3 = log 7 x Put in exponent form7 3 = x Type the base (7) ^ then ( then “the exponent” ) x = 343

10. Practice Lesson 13 Solve for x 3 = log 8 x 6 = log 5 x 0 = log 8 x -3 = log 9 x -2 = log.2 x.01 = log 6 x 1 = log 7 x 0 = log 9 x 512 15,625 1.0014 25 1.02 7 1 13. 14. 15. 16. 17. 18. 19. 20.