Question

Which expressions are equivalent to the one below? Check all that apply. log 2 - log 8 A. log(;) DB. log 4 B. D C. log(2) + -log(3) 8 D D. log 2

Answer 1

$\begin{gathered} log\lparen2)-log\mleft(8\mright)=log\lparen\frac{2}{8}) \\ But \\ \frac{2}{8}=\frac{1}{4} \\ Hence \\ log\lparen\frac{2}{8})=log\lparen\frac{1}{4}) \\ Therefore\text{ } \\ log\lparen2)-log\mleft(8\mright)\text{ is equivalent to log\lparen}\frac{1}{4}) \\ \\ Also \\ log\lparen2)+log\mleft(\frac{1}{8}\mright)=log\mleft(2\ast\frac{1}{8}\mright)=log\mleft(\frac{1}{4}\mright) \\ So \\ log\lparen2)-log\mleft(8\mright)\text{ is equivalente to log\lparen2})+log\mleft(\frac{1}{8}\mright) \\ \\ \end{gathered}$