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Question

If log3x+log3y=2+log32 and log3(x+y)=2, then the values of x and y are

A
x=1,y=8
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B
x=8,y=1
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C
x=3,y=6
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D
x=9,y=3
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Solution

The correct option is C x=3,y=6
log3x+log3y=2+log32=2log33+log32,[log33=1]
As,
[loga+logb=log(ab)] and [xloga=logax]
log3xy=log332+log32
log3xy=log318
xy=18 ....(1)

log3(x+y)=2
x+y=32=9 ....(2)

On solving equation (1) & (2), we get
x=3,y=6

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