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Monday, May 19, 2008

Q) If log a, log b ,log c are in Arithmetic Progression and also loga - log2b ,log2b - log3c , log3c - loga are in Arithmetic Progression then :

1)a, b, c are in AP
2)a, 2b, 3c are in AP
3)a, b, c are the sides of the triangle
4)none of the above


A)
log a, log b ,log c are in AP
loga + logc = 2logb
logac = logb^2
ac = b^2 .....................so a,b,c are in GP.

log a-log 2b ,log2b-log3c , log3c-loga are in AP
loga - log2b + log3c - loga = 2 (log2b - log3c)
log(3c/2b) = 2 (log (2b/3c))
3c/2b = (2b/3c)^2
THUS, 3c/2b = 1
3c = 2b
b = 3c/2

ac= b^2 = 9c^2/4
a = 9c/4
b = 3c/2
c = c

since this is a pythagorean triplet (sum of any 2 is greater than 3rd)
So they are the sides of a triangle.

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