1. Solve the logarithmic equation below. be sure to reject any value that isn't in the domain of the original logarithmic expression. log5(5x - 7) = log5(2x + 5)

2. Use the properties of logarithms to condense the following logarithmic expression: log_cy_cx

Answer Options:

3. What type of transformation would occur with the following logarithmic functions? fix} = laser fix} = IDQoI-K} O A. Reflection about the iiiaxis O B. Horizontal translation to the right c units O G. Horizontal translation to the left c units I D. Reflection about the yaxis 5. Write the formula for the general term (the nth term) of the geometric sequence. 4, 12, 36, 108, 324, . . . O A. an = 4(3)" O B. an = a1 + (3)" O C. an = 4(3n) O D. an = 4(3)7 - 16. Which of the following statements is true about the number e? O A. It's the base of a natural logarithm. O B. It's equal to 2'. O C. It's equal to e9. I D. It's the base of every exponential function. 11. Find the sum of the first six terms of the geometric sequence: -2, -8, -32, ... O A. 2730 O B. -1365 O C. -42 O D. -273012. What's the general formula of the arithmetic sequence 6, 14, 22, 30, 38, . . . ? O A. an = 2n - 1 O B. an = 2n - 8 O C. an = 8n - 1 O D. an = 8n - 213. Use the quotient rule to expand the following logarithmic expression: 7 log3 13 O A. log; 7 + log; 13 O B. log; 13-log; 7 O C. log; 7 -log3 13 O D. log: 7 log; 1314. What type of transformation would occur with the following exponential functions? Original: x] = a\" "' c Transformation: fix} : a\" \"2 O A. Reflection about the xsxis O B. Horizontal shift to the left c units Cl C. Reflection about the yaxis G D. Horizontal shift to the right c units 18. Use the properties of logarithms to expand the logarithmic expression below: 19. Which of the following statements is not correct? 0 A. A necessary;r skill to master before attempting a proof by mathematical inductions is the ability to write three forms of a statement, 31, sk, and SK + 1. O B. Mathematical induction involves first proving a statement 31 and then proving a second statement that 85 implies sk + 1. O 0. Mathematical induction is a method of proof. 0 D. Mathematical induction proves facts about all positive real numbers. 4. A boat leaves the entrance of a harbor and travels 15 miles on a bearing of N 10 E. How many miles north and how manyr miles east from the harbor has the boat traveled? O A. 14.8 miles north and 2.6 miles east O B. 2.6 miles north and 14.8 miles east 0 C. 85.1 miles north and 2.6 miles east 0 D. 15 miles north and 15 miles east 14. A straight trail with a uniform inclination of 13" leads from a lodge at an elevation of 500 feet to a mountain lake at an elevation of 1".500 feet. What's the length of the trail (to the nearest foot]? (3' A. T885 feet O B. 7360 feet (3' (3. 22,652 feet 0 D. 24,2?1 feet 4. complete the following identity: sin i: {sin 2:: + sin 4:] = C]. A. Hams II.\" [:05 25: + :05 4.5:] D B. SIDE x {:05 2x :03 4):} C: G. FEEDS I {ma Ex ans 4):} D D. (:05 .3: {ans Ex + :05 4x} E. A generator produces an alternating current according to the equation 1' = 8 sin 3211: where t is time in seconds and I is the current in amperes. What's the smallest time t such that i = 4? O A. i second 192 O B. l second 64 O G. l second 96 O D. L second 123 COS2 X 7. Complete the following identity: 1- =? 1 + sin x O A. sin x O B. tan x O C. O O D. cot x8. Use the given information to find the exact value of the expression. tan a = 21/20 a lies in quadrant III, cos B = -/13, and B lies in quadrant II. Find sin(a + B)- O A. 345 377 O B. - 135 377 O C. 352 377 OD. 152 37710. Solve the following equation on the interval [0, 2n). tan x + sec x = 1 O A. 0 O B. 4 O C. O D. There's no solution.11. Express the following product as a sum or difference: sin 4x sin 6x O A. NI - (-cos 2x - cos 10x) O B. sin2 (cos 35x2) O C. (cos 2x - cos 10x) O D. (cos 10x - sin 2x)12. Use a calculator to solve the equation on the en the interval [0, 211]. Round to the nearest hundredth of a radian. sin 3.x = -sinx O A. 0, 3.14 O B. D, 0.?9, 2.36, 3.14, 3.93, 5.59 O (11.51431 O D. ID, 1.5T, 3.14, 4.?1 13. An airplane flying faster than the speed of sound creates sound waves that form a cone. If a is the vertex angle at the cone and m is the Mach number for the speed of the plane, then sing = l m (m 3 O A. The set of numbers 1, 2, 3, .. . 8] O B. 3 O C. None O D. The set of numbers 1, 2, 3, . . . 9]5. Translate the following limit notation into a sentence: lim(vx - 2) =0 X-+4 O A. The limit of vx -4 as x approaches 0 equals the number 2. O B. The limit of vx - 2as x approaches 0 equals the number 4. O C. The limit of vx - 4 as x approaches 2 equals the number 0. O D. The limit of vx - 2as x approaches 4 equals the number 0.14. At which points is the function shown in the graph discontinuous? 3+ 0 O -6 6 x O A. -3, -1, 1, 3 O B. 3.5 O C. 1, 3 O D. Nowhere