Chapter 4.4, Problem 76E

To determine

a) To discuss and decide:

Whether the given equation is true for all possible values of the variables.

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

To determine

b) To discuss and decide:

Whether the given equation is true for all possible values of the variables.

${\log }_2\left(x-y\right)={\log }_{2}x-{\log }_{2}y$

To determine

c) To discuss and decide:

Whether the given equation is true for all possible values of the variables.

${\log }_5\left(\frac{a}{b^2}\right)={\log }_{5}a-2{\log }_{5}b$

To determine

d) To discuss and decide:

Whether the given equation is the true for all possible values of the variables.

$\log \cdot 2^z=z\log 2$

To determine

e) To discuss and decide:

Whether the given equation is true for all possible values of the variables.

$\left(\log P\right)\left(\log Q\right)=\log P+\log Q$

To determine

f) To discuss and decide:

Whether the given equation is true for all possible values of the variables.

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

To determine

g) To discuss and decide:

Whether the given equation is true for all possible values of the variables.

${\left({\log }_{2}7\right)}^x=x{\log }_{2}7$

To determine

h) To discuss and decide:

Whether the given equation is true for all possible values of the variables.

${\log }_a{a}^a=a$

To determine

i) To discuss and decide:

Whether the given equation is true for all possible values of the variables.

To determine

j) To discuss and decide:

Whether the given equation is true for all possible value of the variables.

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