Answer:
3
Step-by-step explanation:
we know that
In this problem we can use this equation:
[tex]N=R^{D}[/tex]
Where:
N is the increase factor
R is the reduce factor
D is the dimension
we have
[tex]N=512\\R=8[/tex]
substitute the given values
[tex]512=8^{D}[/tex]
solve for D
Apply log both sides
[tex]log(512)=log(8^{D})[/tex]
Apply property of logarithms
[tex]log(512)=(D)log(8)[/tex]
[tex]D=log(512)/log(8)=3[/tex]
therefore
The dimension is 3
