1. Rewrite each equation in logarithmic form. 4. Rewrite in exponential form. a) 4' = 64 a) log, 49 = 2 b) 128 = 27 b) 5 = log, 32 ( 5 3 = () log 10 000 = 4 25 d) w = log z d) G = 0.25 e) log, 8 = 3 e) 6 = y f) log, 625 = 4 f) 10* = 100 000 g) -2 = log 100 g) 1 = 3-3 h) log, x = 2y 27 h) v = b" 5. Sketch a graph of each function. Then, sketch For belp with questions 2 and 3, refer to Example 2. a graph of the inverse of each function. Label 2. Evaluate each logarithm. each graph with its equation. a) log, 64 a) y = 2* b) y = 4* b) log, 27 For help with questions 6 to 8, refer to Example 4. () log 6. Estimate the value of each logarithm, correct to one decimal place, using a graphical d) log. method. e) log, 125 a) log, 6 f) log, 1024 b) log, 180 g) log, 36' () log, 900 h) log, 81 d) log, 0.0353. Evaluate each common logarithm. 7. Pick one part from question 6. Use a different a) log 1000 graphical method to verify your answer. 8. Evaluate, correct to two decimal places, using b) log 10 a calculator. () log 1 a) log 425 d) log 0.001 b) log 0.000 037 e) log 10-4 c) log 9 f) log 1 000 000 d) log 0.2 g) log e) log 17 100 f) log 99 h) log 10 000 g) log 183 h) log 101010. Evaluate each logarithm. a) log, 3 b) log, 2 () log12 12 d) log1 1 11. a) Make a prediction about the value of log, x for any value of x > 0, x # 1. b) Test your prediction by evaluating several cases. () What can you conclude about the value of log x? Explain your answer using algebraic, numerical, or graphical reasoning.13. The number of visitors to a popular Web site is tripling every day. The time, , in days tor a number, N, of visitors to see the site log N log3 How long will it take until the number of visitors to the Web site reaches each number? a) 1000 b) 1 000 DOOD 15 given by the equation = 15. Chapter Problem Engineers of spacecraft take Care to ensure that the crew is safe from the dangerous cosmic radiation of space. The protective hull of the ship is constructed of a special alloy that blocks radiation according to the equation P = 100(0.2)", where P is the percent of radiation transmitted through a hull with a thickness of x centimetres. a) What thickness of the hull walls will ensure that less than 1% of the radiation will pass through? b) By how much would the thickness of the walls need to be increased in order to reduce the harmful radiation transmission to 0.1%