# How do you use the properties of logarithms to expand log_5 (5/x)?

${\log}_{5} \left(\frac{5}{x}\right) = {\log}_{5} 5 - {\log}_{5} x = 1 - {\log}_{5} x$
${\log}_{5} \left(\frac{5}{x}\right) = {\log}_{5} 5 - {\log}_{5} x$--> Use the property ${\log}_{b} \left(\frac{x}{y}\right) = {\log}_{b} \frac{x}{\log} _ b y$
$= 1 - {\log}_{5} x$ ---> Use property ${\log}_{a} a = 1$