Which expressions are equivalent to the one below? log 2- log 8

Accepted Solution

Answer:A. [tex]\log (2)+\log (\frac{1}{8})[/tex]B. [tex]log (\frac{1}{4})[/tex]Step-by-step explanation:Given expression:[tex]\log 2-\log 8[/tex]Using properties of logarithm we can write the expression in various equivalent forms:1) Using quotient rule [tex][\log a-\log b=log \frac{a}{b}][/tex] :[tex]\log 2-\log 8[/tex]β‡’[tex]log \frac{2}{8}][/tex]Reducing [tex]\frac{2}{8}[/tex] to simple fraction by dividing numerator and denominator by their greatest common factor.β‡’[tex]log \frac{2\div 2}{8\div 2}][/tex]β‡’[tex]log \frac{1}{4}][/tex]2) Plugging in [tex]\log 1[/tex] in the expression as [tex]\log 1=0[/tex]β‡’ [tex]\log 2+\log 1-\log 8[/tex]Using quotient rule again [tex][\log a-\log b=log \frac{a}{b}][/tex] β‡’[tex]\log 2+\log \frac{1}{8}[/tex]