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Question Number 110183 by bemath last updated on 27/Aug/20
   (√★)((be)/(math))(√★)    log _2 (x)+log _3 (x)+log _4 (x)=1     x=?
bemathlog2(x)+log3(x)+log4(x)=1x=?
Answered by Olaf last updated on 27/Aug/20
log_2 x+log_3 x+log_4 x = 1  ((lnx)/(ln2))+((lnx)/(ln3))+((lnx)/(ln4)) = 1  lnx = (1/((1/(ln2))+(1/(ln3))+(1/(ln4))))  x = e^(1/((1/(ln2))+(1/(ln3))+(1/(ln4))))  = e^(1/((3/(2ln2))+(1/(ln3))))
log2x+log3x+log4x=1lnxln2+lnxln3+lnxln4=1lnx=11ln2+1ln3+1ln4x=e1/(1ln2+1ln3+1ln4)=e1/(32ln2+1ln3)
Answered by Aziztisffola last updated on 27/Aug/20
 ln(x)((1/(ln2))+(1/(ln3))+(1/(ln4)))=1   ln(x)(((ln3ln4+ln2ln4+ln2ln3)/(ln2ln3ln4)))=1   ln(x)=((ln2ln3ln4)/(ln3ln4+ln2ln4+ln2ln3))           x   =e^((ln2ln3ln4)/(ln3ln4+ln2ln4+ln2ln3))
ln(x)(1ln2+1ln3+1ln4)=1ln(x)(ln3ln4+ln2ln4+ln2ln3ln2ln3ln4)=1ln(x)=ln2ln3ln4ln3ln4+ln2ln4+ln2ln3x=eln2ln3ln4ln3ln4+ln2ln4+ln2ln3
Answered by john santu last updated on 28/Aug/20
log _2 (x)+((log _2 (x))/(log _2 (3)))+((log _2 (x))/(log _2 (4)))=1  log _2 (x)[1+(1/(log _2 (3)))+(1/2)]=1  log _2 (x) [(3/2)+(1/(log _2 (3)))]=1  log _2 (x)(((log _2 (27)+log _2 (4))/(log _2 (9))))=1  log _2 (x)(((log _2 (108))/(log _2 (9))))=1  log _2 (x)=((log _2 (9))/(log _2 (108)))  log _2 (x)=log _(108) (9)  ⇒ x = 2^(log _(108) (9))  .△
log2(x)+log2(x)log2(3)+log2(x)log2(4)=1log2(x)[1+1log2(3)+12]=1log2(x)[32+1log2(3)]=1log2(x)(log2(27)+log2(4)log2(9))=1log2(x)(log2(108)log2(9))=1log2(x)=log2(9)log2(108)log2(x)=log108(9)x=2log108(9).

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