Chapter 4.4, Problem 41E

PROVE that log, 100 = 2(1 + log; 2)|

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Use properties of logs to simplify the ex- pression log-(x - √²-14) + log7(x + √²-14). Select all that apply 1. log-2 2. 7+log72 3. 1+log72 4. log₂ 7 5. 1+log₂7

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e = exp(1) is called the exponential function. Which of the following are true? (Select all that are correct.) k exp(x) = Σk=0 %/! exp(x) = Ə əx -exp(x) □ exp(x) = exp (2/2) + exp ( ² ) exp(x): = exp (2) exp (2/2) □ In(exp(x)) = x

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9) Fill in the table below, make the graph, and identify the key features. k(x) = logx 1 100 1 10 1 10 100 1000 k(x) ) When are the function values positive? When negative? a) What is the domain of this function? d) For what intervals is this function increasing? b) What is the range of this function? e) For what intervals is this function decreasing? c) x-intercept =, y-intercept = . 4 g) Describe the end behaviors of the function. 3 2 15 20 25 30 35 40 6 50 55 60 6 7o 75 0 6 0 6 100 -3 -5 2.

In Exercises 109112, find the domain of each logarithmic function. 109. f(x) = In(x² - x - 2) 110. f(x) = In(r² – 4x – 12) x + 1 111. х) 3Dlog 112. f(x) = log r + 5, %3D

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