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

Solution:

Given;

$\begin{gathered} \log_(\frac{x}{z^6}) \\ \end{gathered}$

Recall the properties of logarithms;

$\log_(\frac{a}{b})=\log_(a)-\log_(b)$

Thus;

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

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:

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