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