Edit MetaData
8 years, 1 month ago
if x,y,x are in GP and a^x,b^y,c^z are equal then a,c,b are in i)AP ii)GP iii)HP
5 years ago
Take x = 2,y = 6,z = 18 . Now take a = 2^9,b = 2^3,c = 2.It satisfies a^x=b^y=c^z .But it's not GP
8 years, 1 month ago
Let us take x, y, z to be k/r, k, kr respectively.
a^x = b^y = c^y implies a^(k/r) = b^k = c^(kr)
If we take logarithm for all we get,
(k/r) loga = k logb = kr logc
(1/r) loga = logb = r logc
a^(1/r) = b = c^r
Clearly we can observe that a, c, b follow No Progression among AP, GP and HP.
8 years, 1 month ago
Let us take x, y, z to be k/r, k, kr respectively.
a^x = b^y = c^y implies a^(k/r) = b^k = c^(kr)
If we take logarithm for all we get,
(k/r) loga = k logb = kr logc
(1/r) loga = logb = r logc
a^(1/r) = b = c^r
Clearly we can observe that a, c, b follow No Progression among AP, GP and HP.
Hope this helps!
Quick, Easy and Effective Revision
By proceeding you agree to create your account
Free CAT Formulae PDF will be sent to your email address soon !!!