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April 2013 Exam Question 5

K

kylie jane

Member
Hi,

Can someone please let me know where I have gone wrong in my calculations below.

If C(u1,u2,u3,u4) = exp[-{((-lnu1)^a+(-lnu2)^a+(-lnu3)^a+(-lnu4)^a)^(1/a)}]

C= exp[-{((-1)^a((lnu1)^a+(lnu2)^a+ln(u3)^a+ln(u4)^a))^(1/a)}]
=exp[-1*(-1)^(a/a)(lnu1*u2*u3*u4)^(a/a)]
=exp(lnu1*u2*u3*u4)
=u1*u2*u3*u4

If what I've done above is correct then I should get the same as the solutions (95.8%) however I get 92.2%. Have I made a mistake somewhere above??
 
Are you sure that
[(lnu1)^a + (lnu2)^a+(lnu3)^a+(lnu4)^a] = [ln(u1*u2*u3*u4)]^a
????
I mean in gen, (x^a +y^a) is not (x+y)^ a, isnt it!
 
Pretty sure as ln(a) + ln(b) = ln(ab) but I actually think my mistake is due to me applying the power laws for logs incorrectly. ln(a^2)=2*ln(a) but I assumed in my workings above that (ln(a))^2= 2ln(a) which is incorrect... So I think that solves it! :)
 
Thats what i meant! :) ln(a) + ln(b) = ln(ab).
(ln(a))^c + (ln(b))^c would not add up the same way isnt it!
 
Yes, but ln(a^c) + ln(b^c) = ln ((ab)^c). Which is what I had assumed in my workings as I included the power within the log. I understand that (a+b)^c does not equal a^c + b^c.
 
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