Chapter 5.5, Problem 131E

In Exercises125-132, match the logarithmic expression on the left with an equivalent logarithmic expression on the right. Assume $\mathit{x},\mathit{ }\mathit{y},\mathit{ }\mathit{z},\mathit{ }\mathit{a}\mathit{n}\mathit{d}\mathit{ }\mathit{w}$are positive number.

  $-{\log }_{300}{x}^{100}{y}^{200}$

a. $100{\mathrm{l}\mathrm{o}\mathrm{g}}_{500}w+200{\mathrm{l}\mathrm{o}\mathrm{g}}_{500}x-300{\mathrm{l}\mathrm{o}\mathrm{g}}_{500}z-400{\mathrm{l}\mathrm{o}\mathrm{g}}_{500}y$

b. $100{\mathrm{l}\mathrm{o}\mathrm{g}}_{500}w+200{\mathrm{l}\mathrm{o}\mathrm{g}}_{500}x+300{\mathrm{l}\mathrm{o}\mathrm{g}}_{500}z-400{\mathrm{l}\mathrm{o}\mathrm{g}}_{500}y$

c. $\frac{1}{100}{\mathrm{l}\mathrm{o}\mathrm{g}}_{200}x+\frac{1}{100}{\mathrm{l}\mathrm{o}\mathrm{g}}_{200}y$

d. ${\mathrm{l}\mathrm{o}\mathrm{g}}_{200}x+\frac{1}{100}{\mathrm{l}\mathrm{o}\mathrm{g}}_{200}y$

e. $200{\mathrm{l}\mathrm{o}\mathrm{g}}_{300}x+100{\mathrm{l}\mathrm{o}\mathrm{g}}_{300}y$

f. $100{\mathrm{l}\mathrm{o}\mathrm{g}}_{300}x+200{\mathrm{l}\mathrm{o}\mathrm{g}}_{300}y$

g. ${\mathrm{l}\mathrm{o}\mathrm{g}}_{300}{x}^{100}+{\mathrm{l}\mathrm{o}\mathrm{g}}_{300}{y}^{200}$

h. ${\mathrm{l}\mathrm{o}\mathrm{g}}_{300}\frac{1}{x^{100}}+{\mathrm{l}\mathrm{o}\mathrm{g}}_{300}\frac{1}{y^{200}}$