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Question

The solution set of the equation logx3log3x3=log9x3 is similar to which of the following options :
  1. logx3log3/x3=logx/93
  2. (log3x)2=2
  3. log2(12log2log3x2)=0
  4. 2logx3=1


Solution

The correct options are
A logx3log3/x3=logx/93
B (log3x)2=2
logx3log3x3=log9x3x>0,3x>0>9x>0  &x,3x,9x11log3xlog33x=1log39xlog3x(1+log3x)=2+log3x(log3x)2=2

x={32,32}


logx3log3/x3=logx/93log3x(1log3x)=log3x2(log3x)2=2x=3±2

log2(12log2log3x2)=0
x=±9


2logx3=1x=32

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