Purdue Global University Mathematics Questions

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WnmmlB2124

Mathematics

Purdue Global University

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Question 1 (Multiple Choice Worth 5 points) (05.02 MC) Rewrite 3x = 243 as a logarithmic equation. log3243 = x logx243 = 3 log3x log243x = 3 Question 2(Multiple Choice Worth 5 points) (05.02 MC) Which expression is equivalent to 3 log₂ x − 4 log₂ y + 2 log2 z? ○ 108: (++) O 7² O O log2 (1) O WORE (1) ○ 1080 (2) = 243 Question 3(Multiple Choice Worth 5 points) (06.01 MC) The girls group rented 2 canoes and 3 inner tubes for a total cost of $80. The boys group rented 1 canoe and 7 inner tubes for a total cost of $95. What is the cost to rent 1 canoe? $10 $15 $25 $18 3 0 0Question 4(Multiple Choice Worth 5 points) (05.05 MC) Choose the function to match the graph. -2- 0 -2- -5 -6- --7- -8- --9. -10- -11 12+ f(x) = log x + 5 f(x) = log x - 5 f(x) = log (x + 5) Of(x) = log (x - 5) 8 9 10 11 12 13 14 0Question 5(Multiple Choice Worth 5 points) (05.06 MC) Using the graph of the function g(x) = log5 (x − 3), what are the x-intercept and asymptote of g(x)? The x-intercept is 4, and the asymptote is located at x = 3. The x-intercept is 3, and the asymptote is located at x = 4. The x-intercept is 4, and the asymptote is located at y = 3. The x-intercept is 3, and the asymptote is located at y = 4. Question 6(Multiple Choice Worth 5 points) (06.02 MC) Given the following system of equations and its graph below, what can be determined about the slopes and y-intercepts of the system of equations? ++ -2 -3 -6-5-4-3-2 =1 1 2 3 4 5 6 7 4 -5 -6 -7 y 10 -9 -10 -11 X 4x + 2y = -2 x - 3y = 24 The slopes are different, and the y-intercepts are different. The slopes are different, and the y-intercepts are the same. The slopes are the same, and the y-intercepts are different. The slopes are the same, and the y-intercepts are the same. 0 0Question 7(Multiple Choice Worth 5 points) (05.01 MC) If $300 is invested at a rate of 6% per year and is compounded quarterly, how much will the investment be worth in 12 years? Use the compound interest formula A - P| 1+. 1A=P(1+)" $145.23 $358.69 $613.04 nt $618.41 0Question 9(Multiple Choice Worth 5 points) (05.05 MC) What are the y-intercept and the asymptote of g(x) = 3x - 5? (0, -5); y = 3 (0, -2); y = 5 (0, -4); y = -5 (0,5); y = -3 Question 10(Multiple Choice Worth 5 points) (05.01 MC) If $535 is invested at an interest rate of 7% per year and is compounded continuously, how much will the investment be worth in 15 years? Use the continuous compound interest formula: A = Pert. $1,625.93 $1,528.84 $666.65 $573.79 15
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Explanation & Answer

View attached explanation and answer. Let me know if you have any questions.Solutions to the questions in the images.

1.
Take a base 3 logarithm on both sides:
log 3 3𝑥 = log 3 243
Use the identity property log 𝑎 𝑎 𝑥 = 𝑥:
log 3 243 = 𝑥
2.
Use the exponent property of logarithms:
log 2 𝑥 3 − log 2 𝑦 4 + log 2 𝑧 2
Use the product and quotient pr...


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