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Question

The number of real value(s) of x satisfying log1/3(2(12)x1)=log1/3((14)x4) is

A
0
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B
1
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C
2
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D
4
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Solution

The correct option is B 1
log1/3(2(12)x1)=log1/3((14)x4)
For the log to be defined, we get
2(12)x1>0 and (14)x4>0(12)x>12 and (14)x>4(12)x>(12)1 and (14)x>(14)1x<1 and x<1 (14,12<1)x<1(1)

log1/3(2(12)x1)=log1/3((14)x4)2(12)x1=(14)x42(12)x1=(12)2x4(12)2x2(12)x3=0

Assuming (12)x=t
t22t3=0(t+1)(t3)=0t=1,3(12)x=3 [(12)x>0]

Taking log on both sides, we get
xlog12=log3x=log3log2x=log23

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