[tex]\text{Log}_4(\frac{64}{x})=3-Log_4x[/tex]
Here, we want to use logarithmic properties to expand the given expression;
We are going to use the following properties of logarithms;
[tex]\text{Log}_a(\frac{x}{y})=Log_ax-Log_ay[/tex]
Applying that in the case of the question, we have;
[tex]\text{Log}_4(\frac{64}{x})=Log_464-Log_4x[/tex]
Furthermore;
[tex]Log_aa^2=2Log_aa_{_{}}_{}[/tex]
Kindly recall that;
[tex]64=4^3[/tex]
Thus, we have;
[tex]\text{Log}_464=Log_44^3=3Log_44[/tex]
Also, an important logarithmic property to use is that;
[tex]Log_aa=1_{}[/tex]
Thus, we have;
[tex]3og_44\text{ = 3}[/tex]
So finally we have;
[tex]\text{Log}_4(\frac{64}{x})=3-Log_4x[/tex]
