Logarithms

15 Points Per Correct Answer - No time limit  

1. Let's say that James visits his doctor for a routine checkup, and for some obscure and somewhat unethical reason he decides to give him his cholesterol level in logarithmic form. In his chicken scratch he gives him this equation: log_x 25 + log_x 16 = 2 (The x is the base of the log) Take the value of x and multiply it by 10 to get your cholesterol level. What is James' cholesterol level? 100 250 150 200

2. In a zoo there are log (10000000000) chimpanzees. Each of the chimps live in a suitable environment. The zoo receives log_2 (64) new chimps, but they do not have enough space for each of them. Assume that the zoo provides each chimp 80 square feet of land (no more, no less). Including the chimps the zoo already has, how big will the zoo be after they renovate to hold the new chimps? 1360 square feet 1200 square feet 1280 square feet 1120 square feet

3. Sally and John have recently broken up from a relationship. They're in the phase where the two try to avoid each other. In school, John walks the path y=x+10 to his next class, which Sally travels a path of log (x). Will the two ever cross paths during this time? (both paths are on the Cartesian plane) Yes No

4. Marc is a cryptographer who been trying to solve the following code: XDC CX UDWLQ Marc was given the key for the code, but he has trouble working with logarithms. log_7(log_2(log_3 x)) = 0 Take the value of x and shift the letter in the code that many places back in the alphabet to decode the message. What is the code that Marc is trying to solve? elk or moose day of death out to lunch lay on cover

5. Diana is a teacher's assistant who must grade tests for a math professor. The professor gives Diana the following instructions: "After grading, you can find the score of the test by counting the amount of questions answered correctly and multiplying that by the numerical value of (5/4) - (log_(log_2 256) 8) (log_2 256 is the base of log_8) With the number of correct multiplied, you can then divide that by 0.2. That should give you the percentage of the test with the kicked in curve. When you're done just write the letter grade on the test. Remember...an "A" is anything above 89.5%, "B" 79.5%-89%, "C" 69.5%-79.5%, "D" 59.5%-69.5%, and "F's" are the rest." On the last test Diana is grading there were a total of 48 questions answered correctly. What letter grade should Diana put on the test? D B A C

6. Waking up, Frank suddenly remembers that today is his father's birthday, and he hasn't prepared for a party yet. To his luck, he doesn't remember his father's age, and decides to ask his mother about it. His mother is shocked that her very own son cannot remember his father's own age. Instead of giving him Dad's age, she says that Frank needs to redeem himself by working extra to prepare for Dad's special day, and gives him this equation that can be solved to find Dad's age: log_209 (2x) = log_209 (x+51) How old is Frank's father? 50 51 49 48

7. In an odd raffle contest, you need to get four tickets with the same value on them to win $1000. If you get three, you win $100, and you win $10 if you get two of the same. Of course, you don't win anything if you don't get any matching tickets. Monica participates in this raffle and draws the following four tickets: 3 (log_3 (12))*(log_12 (27)) (log_12 (144))*(log_12 (12)) 1/(log_27 3) How much money does Monica win? $0 $1000 $100 $10

8. Andrei is going through a logarithm test. Allowed to use a graphing calculator, he encounters the following problem: Give the numerical value of (log_3 90) to the nearest thousandth. Andrei knows that the only way to evaluate this is to use his calculator; however, the calculator is able to only evaluate base-10 logs. The formula that can be used to help Andrei to get the logs into base ten so that he can solve the problem is the ________ of base formula. Answer: (One Word, starts with "c")

9. Michelle has 8^(log_2 x) dollars and wants to buy a necklace that costs $64. If Michelle has exactly enough money to buy the necklace, what does x equal? 4 10 2 8

10. George is in a math contest with 100 other contestants including himself. After competing, George is in the xth place: log x + log 2x = 2 - log 2 Where did George place in the competition? 4th 5th 3rd 2nd