Question

hello!

7.115 :

if a^x=b^y=c^z and x,y,z are inG.P. then log a, log b, log c are in ??​

Answer 1

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.

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Answer 2

Take x.,y,z as any gp, say 3, 9,27 respectively. Now to a^x=b^y=c^z take a,b, cas any descending gp say 27, 9,3. Hwnce the correct option is GP.

or

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 it helps u mark as brainliest please