Trigonometry Homework #6 due 3-23

For each equation below, determine whether it is true for all possible values of the variables or not and explain your answer. Ignore values of the variables for which any term is undefined.

1. $\log \left (\frac{x}{y} \right )= \frac{\log{x}}{\log{y}}$

2. $\log_2 (x-y) = \log_2 x - \log_2 y$

3. $\log_5 \left (\frac{a}{b^2} \right )= \log_5 a - 2 \log_5 b$

4. $\log 2^z = z \log 2$

5. $(\log P)(\log Q)= \log P + \log Q$

6. $\frac{\log a}{\log b}= \log a - \log b$

7. $(\log_2 7)^x =x \log_2 7$

8. $\log_a a^a =a$

9. $\log (x-y) = \frac{\log x}{\log y}$

10. $-\ln \left (\frac{1}{A} \right )=\ln A$

Trigonometry Homework #5 due 3-16

While in chem lab, you find a sandwich behind some beakers. You’re very hungry, having missed lunch, and are thinking about eating this sandwich that you found, but you don’t know how long it’s been there. Using a handy Geiger counter, you find that the sandwich has 98% of its carbon-14 remaining. Would you eat the sandwich? Explain your answer algebraically.

Calculus Homework #1 due Thursday, February 12th

While in chem lab, you find a sandwich behind some beakers. You’re very hungry, having missed lunch, and are thinking about eating this sandwich that you found, but you don’t know how long it’s been there. Using a handy Geiger counter, you find that the sandwich has 98% of its carbon-14 remaining. Would you eat the sandwich? Explain your answer algebraically.

Project #3: Chemistry Sandwich

While in chem lab, you find a sandwich behind some beakers. You’re very hungry, having missed lunch, and are thinking about eating this sandwich that you found, but you don’t know how long it’s been there. Using a handy Geiger counter, you find that the sandwich has 98% of its carbon-14 remaining. Would you eat the sandwich? Explain your answer algebraically.

Solutions to logarithmic equations classwork

1. $x=-\log 4$

2. $x=\frac{\ln 200-1}{2}$

3. $x=-\ln 4$

4. $x=\ln 3$

5. $x=\frac{1}{100}$

6. $x=-e^2+3$

7. $x=5$

8. $x=\frac{-1+\sqrt{9+4e}}{2}$

9. $x=43046721$

10. $x=\{101,1.1\}$

11. $x=64$

12. $x=\log_2 3$