SOLUTION: 3^x=27^a+b and a^2-b^2/(a-b)=5. What is X A)6 B)9 C)12 D15

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Question 1143084: 3^x=27^a+b and a^2-b^2/(a-b)=5. What is X
A)6
B)9
C)12
D15
Answer by greenestamps(13200) About Me  (Show Source):
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Use parentheses where required! Don't make us correct your statement of the problem.

27^(a+b) (27%5E%28a%2Bb%29); not 27^a+b (27%5Ea%2Bb)
(a^2-b^2)/(a-b) (%28a%5E2-b%5E2%29%2F%28a-b%29); not a^2-b^2/(a-b) (a%5E2-b%5E2%2F%28a-b%29)

So

3%5Ex+=+27%5E%28a%2Bb%29
%28a%5E2-b%5E2%29%2F%28a-b%29+=+5

The division in the second equation gives you the value of (a+b).

27^(a+b) is (3^3)^(a+b) = 3^(3(a+b)) = 3^x, so x = 3(a+b); and you know what (a+b) is.

You should get answer D....