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Name: __________________________ Date: _____________ 1. Use a graphing utility to graph the function. A) B) C) D) E) Page 1 2. Identify the x-intercept of the function y = 5 + log 2 x . A) 32 B) 1 32 C) –5 D) 10 E) The function has no x-intercept. 3. Evaluate the function f ( x) = − 2.504 ln x at x = 182.55 . Round to 3 decimal places. (You may use your calculator.) A) –6.125 B) 13.038 C) –13.038 D) 2.079 E) undefined 4. Rewrite the logarithmic equation log 6 A) 636 = – 2 B) 61/ 36 = – 2 1 6 –2 = 36 C) D) ⎛ 1 ⎞ ⎜ ⎟ ⎝ 36 ⎠ E) 6 –2 = − –2 1 = – 2 in exponential form. 36 =6 1 36 Page 2 5. The pH of an acidic solution is a measure of the concentration of the acid particles in the solution, with smaller values of the pH indicating higher acid concentration. In a laboratory experiment, the pH of a certain acid solution is changed by dissolving over-the-counter antacid tablets into the solution. In this experiment, the pH changes according to the equation ⎛ x ⎞ pH = 5.0 + log ⎜ ⎟, ⎝ 0.1 − x ⎠ where x is the number of grams of antacid added to the solution. Use a graphing utility to graph the pH function on the interval 0 < x < 0.1. A) B) C) D) Page 3 E) 6. Write the exponential equation e5 / 2 = 12.1825... in logarithmic form. A) ⎛5⎞ 2.303log ⎜ ⎟ = 12.1825... ⎝2⎠ B) 5 log10 (12.1825...) = 2 C) 5 ⎛ ⎞ ln ⎜ ⎟ = 12.1825... ⎝2⎠ D) 5 ln (12.1825...) = 2 E) 12.1825... ln 5 = 2 7. Identify the the value of the function f ( x) = log 2 . 2 A) 2 B) 102 C) 21/2 D) 1 2 E) undefined Page 4 8. Write the logarithmic equation ln 5 = 1.609... in exponential form. A) e1.609... = 5 B) 105 = 1.609... C) 2.303 e1.609... = 5 D) 2.303 ×105 = 1.609... E) e5 = 1.609... 9. Solve the equation log(1 − x) = log(1000) for x using the One-to-One Property. A) 1001 B) –999 C) –1001 D) –2 E) The equation has no solution. 10. Identify the x-intercept of the function f ( x) = 4 ln( x − 1) . A) x = 1 B) x = 0 C) x = 4 D) x = 2 E) The function has no x-intercept. Page 5 Answer Key 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. B B C C E D D A B D Page 6