Answer:
The proprierties are explained in the step-by-step explanation.
Step-by-step explanation:
We have the following logarithm proprierty:
[tex]\log{\frac{a}{b}} = \log{a} - \log{b}[/tex]
And
[tex]\log{1} = 0[/tex]
So, we apply these proprierties:
[tex]\log{\frac{1}{x}} = \log{1} - \log{x} = 0 - \log{x} = -\log{x}[/tex]
Since the domain of [tex]\log{x}[/tex] is [tex]x > 0[/tex], we have that
[tex]\log{\frac{1}{x}} = -\log{x}, x > 0[/tex]
