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Question

If 1,logyx,logzy,15logxz are in A.P. , then

A
z3=x
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B
x=y1
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C
z3=y
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D
x=y1=z3
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E
All the above
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Solution

The correct option is E All the above
Let d be the common difference of the A.P.
Then,
logyx=1+d
x=y1+d ----- ( 1 )

logzy=1+2d
y=z1+2d ------ ( 2 )

15logxz=1+3d
z=x(1+3d)15 ------ ( 3 )

x=y1+d=z(1+2d)(1+d)=x(1+d)(1+2d)(1+3d)15

(1+d)(1+2d)(1+3d)=15

6d3+11d2+6d+16=0

(d+2)(6d2d+8)=0

d=2

Substituting value of d we get,

x=y1=z3=x13 or

x=y1=z3,y=z3


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