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

d

step-by-step explanation:

by observation, we can see that the the graph is simply the graph of y = |x| that has been shifted 4 units downwards and 3 units to the left.

we can recognize in choice d :

y = | x + 3 |   - 4 (rewriting in general form)

y = | x - (- 3) |   - 4

the "-4 " term means   that the graph has been shifted by 4 units in the negative y direction

the "-3 " term means   that the graph has been shifted by 3 units in the negative x direction

this matches our observation of the graph described above.

it has the same slope and a different y-intercept

hope this : )