Question

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

Answer 1

Answer:

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

Step-by-step explanation:

We have the following logarithm proprierty:

$\log{\frac{a}{b}} = \log{a} - \log{b}$

And

$\log{1} = 0$

So, we apply these proprierties:

$\log{\frac{1}{x}} = \log{1} - \log{x} = 0 - \log{x} = -\log{x}$

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

$\log{\frac{1}{x}} = -\log{x}, x > 0$