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Question

If 2x+y=6y and 3x1=2y+1, then the value of log3log2xy will be

A
1
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B
log23log32
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C
log32
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D
none of these
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Solution

The correct option is C log32
2x+y=6y(x+y)log2=ylog6(x+y)log2=y(log2+log3)
xlog2=ylog3 ...(1)
3x1=2y+1(x1)log3=(y+1)log2
xlog3ylog2=log3+log2 ...(2)
From (1) & (2)
x=log3log3log2
y=log2log3log2
xy=log3log2log3log2log3log2xy=log32

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