If 1, log x (base y), log y (base z), -15 log z (base x)

are in AP, then

a) z^3 = x

b) x = y^-1

c) z^-3 = y

d) all of these

Regards

Sreedhar

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- April 30th 2010, 08:05 PMyshridharProgressions
If 1, log x (base y), log y (base z), -15 log z (base x)

are in AP, then

a) z^3 = x

b) x = y^-1

c) z^-3 = y

d) all of these

Regards

Sreedhar - April 30th 2010, 11:53 PMhollywood
Let the common difference be d. Then the progression is 1, d+1, 2d+1, and 3d+1, so

Combining the first two gives , and equating exponents gives (3d+1)(2d+1)(d+1)=-15, with the only solution d=-2.

- Hollywood - May 1st 2010, 06:48 AMSoroban
Hello, yshridhar!

*Lovely work, Hollywood!*

Quote:

. .

Hollywood had: .

Then we have:

. .

. .

. .

Answer: .

- May 1st 2010, 07:31 PMyshridhar
Thanks alot Hollywood for such a simple solution. I am banging with logarithms formulae for this sum.

Regards

Sridhar