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Question

If x>0 and log3x+log3x+log3x4+.......=4, then x equals


A

9

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B

81

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C

1

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D

27

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Solution

The correct option is A

9


Explanation for the correct answer:

Finding the value of x:

Given,

log3x+log3x+log3x4+.......=4log3x+12log3x+14log3x+......=4[logxn=nlogx]log3x1+12+14+....=4log3x11-12=4[Sn=a1-r,whereaisfirsttermandriscommonratio.]log3x2=4log3x=42log3x=2x=32[iflognx=k,thenx=kn]x=9

Hence, the correct option is A.


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