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How to solve it? It is from sequence and series From Geometric progression part

How to solve it? It is from sequence and series From Geometric progression part

Question Image
Grade:12th pass

1 Answers

Shahid
74 Points
4 years ago
Given : [logx/1] = [logy/2] = [logz/3]
To Prove: x,y,z are in G.P.
 
Proof:
Let [logx/1] = [logy/2] = [logz/3] = k
Therefore,
logx = k                                                                           
logy = 2k = 2 x logx  = log(x2)  … Thus, y  = x2                                                            ----{1}
logz = 3k = 3 x logx  = log(x3) …. z = x3                                                                        -----{2}
 
from {1}, {2}
(x,y,z) = (x,x2,x3)...
Therefore, they are in G.P. with the common ratio “x”

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