if k,n,x, and y are positive numbers satisfying
x^ -4/3=k^ -2 and y^4/3 =n^2 ,what is (xy)^-2/3
in terms of n and k ?
A)1/nk
B)n/k
C)k/n
D)nk
E)1
math problem!
2006-10-21 7:37 pm
回答 (2)
2006-10-21 7:56 pm
✔ 最佳答案
x^-4/3=k^-2x^(-4/3*1/2)=k^(-2*1/2)
x^-2/3=k^-1
x^-2/3=1/k------------------(1)
y^4/3=n^2
y^(4/3*-1/2)=n^(2*-1/2)
y^-2/3=n^-1
y^-2/3=1/n------------------(2)
(1)*(2), (xy)^-2/3=1/n*1/k
(xy)^-2/3=1/nk
The answer is A.
2006-10-21 8:47 pm
Or using log approach:
x^ -4/3=k^ -2
log x = (3/2) * log k ------1
y^4/3 =n^2
log y = (3/2) * log n ---------2
Consider log (xy)^-2/3
=(-2/3) * (log x + log y)
=(-2/3) * [(3/2) * log k + (3/2) * log n] //sub 1 & 2 into the equation
= - (log k + log n)
= - log (kn)
= log (1/kn)
Hence log (xy)^-2/3 = log (1/kn)
which implies (xy)^-2/3 = 1/kn
Therefore the answer is A
x^ -4/3=k^ -2
log x = (3/2) * log k ------1
y^4/3 =n^2
log y = (3/2) * log n ---------2
Consider log (xy)^-2/3
=(-2/3) * (log x + log y)
=(-2/3) * [(3/2) * log k + (3/2) * log n] //sub 1 & 2 into the equation
= - (log k + log n)
= - log (kn)
= log (1/kn)
Hence log (xy)^-2/3 = log (1/kn)
which implies (xy)^-2/3 = 1/kn
Therefore the answer is A
收錄日期: 2021-04-13 15:56:48
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