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Question

If (x,y) is the solution of the following equations (2x)log2=(3y)log3and3logx=2logy, then x is equal to


A

16

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B

13

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C

12

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D

6

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Solution

The correct option is C

12


Explanation for the correct option.

The first equation is (2x)log2=(3y)log3

By taking log on the both sides we get

log2log2+logx=log3log3+logy....1 (by product and power property of log)

The second equation is 3logx=2logy

By taking log on both sides we get;

logxlog3=logylog2(bypowerproperty)⇒logxlog3log2=logy

By substituting the value of logy in 1, we get

log2log2+logx=log3log3+logxlog3log2

⇒log22+log2logx=log32+log32logxlog2⇒log22-log32=log32logxlog2-log2logx⇒log22-log32=logxlog32-log22log2⇒logxlog2=-1⇒logx=-log2⇒x=12

Hence, option C is correct.


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