Answer:
The product of x and y is 8[tex]8[/tex]
Step-by-step explanation:
If [tex]\log_{5\sqrt{5}}125=x[/tex], then the exponential form is:
[tex]125=(5\sqrt{5})^x[/tex]
[tex]\implies 5^3=(5)^{\frac{3x}{2}}[/tex]
[tex]\implies 3=\frac{3x}{2}[/tex]
[tex]\implies 6=3x[/tex]
[tex]\implies x=\frac{6}{3}=2[/tex]
Also if, [tex]\log_{2\sqrt{2}}64=y[/tex], then the exponential form is:
[tex]64=(2\sqrt{2})^y[/tex]
[tex]\implies 2^6=(2)^{\frac{3y}{2}}[/tex]
[tex]\implies 6=\frac{3y}{2}[/tex]
[tex]\implies 12=3y[/tex]
[tex]\implies y=4[/tex]
The product of x and y is [tex]xy=2\times 4=8[/tex]
