Question

Use the properties of logarithms to expand logxz6.Each logarithm should involve only one variable and should not have any exponents. Assume that all variables are positive.

Answer 1

Given;

`\begin{gathered} \log_((x)/(z^6)) \\ \end{gathered}`

Recall the properties of logarithms;

`\log_((a)/(b))=\log_(a)-\log_(b)`

Thus;

`\log_\text{ }((x)/(z^6))=\log_\text{ }(x)-\log_{\text{ }}(z^6)`

Recall the power property of logarithm;

`\log_{\text{ }}(a^b)=b\log_{\text{ }}(a)`

Then;

`\log_{\text{ }}(x)-\log_{\text{ }}(z^6)=\log_{\text{ }}(x)-6\log_{\text{ }}(z)`

ANSWER:

`\begin{equation*} \log_{\text{ }}(x)-6\log_{\text{ }}(z) \end{equation*}`