SOLUTION: given that , 10^0.48 = x,10^0.70 =y and x^z =y^2, then the value of z is a)1.45 b)1.88 c)2.9 d)3.7
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Question 1039520
:
given that , 10^0.48 = x,10^0.70 =y and x^z =y^2, then the value of z is
a)1.45
b)1.88
c)2.9
d)3.7
Answer by
Theo(13342)
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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.
