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If-3-log-3x-4-log-4x-find-x-

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Question Number 1304 by 314159 last updated on 20/Jul/15
If 3^(log 3x) =4^(log 4x) , find x.
If3log3x=4log4x,findx.
Answered by Rasheed Soomro last updated on 20/Jul/15
3^(log 3x) =4^(log 4x) Taking logarthm of both sides log(3^(log 3x) )=log(4^(log 4x) ) log 3x .log 3=log 4x.log 4 (log 3+log x).log 3=(log 4+log x).log 4 (log 3)^2 +log 3.log x=(log 4)^2 +log 4.log x log 4.log x−log 3.log x=(log 3)^2 −(log 4)^2 log x.(log 4−log3)=(log 3+log 4)(log 3−log 4) −log x(log 3−log 4)=(log 3+log 4)(log 3−log 4) −log x=log 3 +log 4 log (x^(−1) )=log(3×4) (1/x)=12 x=(1/(12))
3log3x=4log4xTakinglogarthmofbothsideslog(3log3x)=log(4log4x)log3x.log3=log4x.log4(log3+logx).log3=(log4+logx).log4(log3)2+log3.logx=(log4)2+log4.logxlog4.logx−log3.logx=(log3)2−(log4)2logx.(log4−log3)=(log3+log4)(log3−log4)−logx(log3−log4)=(log3+log4)(log3−log4)−logx=log3+log4log(x−1)=log(3×4)1x=12x=112

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