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