Question 1039520
you are given that:


x = 10^(.48)
y = 10^(.7)
x^z = y^2.


replace x with 10^(.48) and replace y with 10^(.7) and you get:
(10^(.48))^z = (10^(.7))^2


since (a^b)^c = a^(b*c), you get:


(10^(.48))^z = (10^(.7))^2 becomes 10^(.48*z) = 10^(.7*2)
simplify this to get 10^(.48*z) = 10^(1.4)


this is true if and only if .48*z = 1.4.
solve for z to get z = 1.4/.48 = 2.91666666667
this rounds to z = 2.9


that would be selection c.


you would confirm by replacing z with 2.91666666667 in the original equation to get:


(10^.48)^(2.91666666667) = 25.11886432
(10^.7)^2 = 25.11886436


they're the same, so the the solution is correct.


z = 2.9 rounded to the nearest tenth.