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]
⇒[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.
⇒[tex]log \frac{2\div 2}{8\div 2}][/tex]
⇒[tex]log \frac{1}{4}][/tex]
2) Plugging in [tex]\log 1[/tex] in the expression as [tex]\log 1=0[/tex]
⇒ [tex]\log 2+\log 1-\log 8[/tex]
Using quotient rule again [tex][\log a-\log b=log \frac{a}{b}][/tex]
⇒[tex]\log 2+\log \frac{1}{8}[/tex]
