Question

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

Answer 1

The proprierties are explained in the step-by-step explanation.

Explanation:

We have the following logarithm proprierty:

`\log{(a)/(b)} = \log{a} - \log{b}`

And

`\log{1} = 0`

So, we apply these proprierties:

`\log{(1)/(x)} = \log{1} - \log{x} = 0 - \log{x} = -\log{x}`

Since the domain of
`\log{x}` is
`x > 0`, we have that

`\log{(1)/(x)} = -\log{x}, x > 0`