Use the properties of logarithms to expand each logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator.

1/5log2(x)+4/5log2(y)-4/5

Step-by-step explanation:

=log2{(xy^4/16)}^1/5

=1/5×log2(xy^4/16)

=1/5×{log2(xy^4)-log2(16)}

=1/5×{log2(x)+log2(y^4)-log2(2^4)}

=1/5×{log2(x)+log2(y^4)-4)} ( as loga(a^x)=x)

=1/5×log2(x)+1/5log2(y^4)-4×1/5 (distribute 1/5 through the parentheses)

=1/5×log2(x)+1/5×4log2(y)-4/5

=1/5log2(x)+4/5log2(y)-4/5

answer: evaluate the objective function at each vertex to determine which - and -values, if any, maximize or minimize the function. example: find the minimum value and maximum value of the objective function f ( x , y ) = 4 x + 5 y , subject to the following constraints