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Question

If (3x)log3=(4y)log4 and (4)logx=(3)logy, then x equals


A

1/3

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B

1/2

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C

1/4

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D

7

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Solution

The correct option is A

1/3


(3x)log3=(4y)log4log3 log33x=log4 log34ylog43(log33+log3x)=log34+log3y (1)4logx=3logylogx.log4=logy.log3log3x=log4y (2)(2) in (1)log43 (1+log4y)=log34+log4y log34log43 (1+log4y)=log34(1+log4y)(log43log34)(1+log4y)=0log4y=1=log3xx=31x=13


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