Latest Elitmus Aptitude Question SOLUTION: log(xy^3)=a log(x^2y)=b find the value of logy/logx

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(#M40054831) ELITMUS Numerical Ability question Logarithm Keep an EYE

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

find the value of logy/logx

Asked In Elitmus Farid Ahmad (9 years ago)

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VIVEK KUMAR  (9 years ago)

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)

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sultana mirdey  (9 years ago)

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)

Is this solution Helpfull? Yes (4) | No (1)  

Azhar Syed  (9 years ago)

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

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jitendra kumar  (9 years ago)

log(y)/log(x)=(2a-b)/(3b-a)

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