log(xy^3)=a
log(x^2y)=b

find the value of logy/logx

• log x +logy^3=a
  log x + 3*log y=a--------1
  now take second expression
  log x^2 + log y=b
  2*logx + log y=b---------2
  multiply equation 1 by 2 and solve the equation 3 & 2
  2*log x + 6*log y=2*a-----3
  2*logx + log y=b
  --------------------------
  5*log y= 2a-b
  log y= (2a-b)/5-----------4
  
  put the value of 4 in 2, we will get
  2*logx + (2a-b)/5 =b
  2*logx = b-(2a-b)/5
  2*logx = (5b-2a+b)/5
  2*logx = (6b-2a)/5
  2*logx = 2(3b-a)/5
  log x= (3b-a)/5------------5
  
  now,
  log y/log x= (2a-b)/(3b-a)
  
  
• 10 years agoHelpfull: Yes(6) No(4)
• log(xy^3)=a
  logx+log(y^3)=a
  logx+3logy=a-----------1
  next
  log(x^2y)=b
  log((x^2)+logy=b
  2logx+logy=b-----------2
  equation 1 divided by 2
  (logx+3logy)/(2logx+log y)=a/b
  now divided by logx
  (1+3t)/(2+t)=a/b where t=logy/logx
  t=(2a-b)/(3b-a)
  logy/logx=(2a-b)/(3b-a)
• 10 years agoHelpfull: Yes(4) No(1)
• Answer is (2ay-b)/3b
  
  log(x)+3log(y)=a........eqn1
  2ylog(x)=b..................eqn2
  
  dividing eqn1/eqn2 we get;
  1/2y + 3log(y)/2ylog(x) = a/b
  
  solving further log(y)/log(x)= 92ay-b0/3b
• 10 years agoHelpfull: Yes(0) No(0)
• log(y)/log(x)=(2a-b)/(3b-a)
• 10 years agoHelpfull: Yes(0) No(0)