deyaalsalmi6126 deyaalsalmi6126
  • 22-10-2019
  • Mathematics
contestada

33. Use properties 1–6 of logarithms to establish property 7: log 1/x = −log(x) for all x > 0.

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joaobezerra joaobezerra
  • 23-10-2019

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]

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