Grade 11Algebra
ln2x^ln2=ln3y^ln33^lnx=2^lnythen find the values of x and y
ln2x^ln2=ln3y^ln3
3^lnx=2^lny
then find the values of x and y
2 Answers
kartik
(2x)^ln2 = (3y)^ln3
3^lnx= 2^lny
taking log on both sides
ln2 ln2x = ln3 ln3y lnx ln3= lny ln2
using the 2 equations eleminate one variable and solve for other
Suraj
(2x)
ln2
=(3y)
ln3
Taking ln both side,
⇒(ln2)ln(2x)=(ln3)ln(3y)
⇒(ln2)(ln2+lnx)=(ln3)(ln3+lny)
⇒
(lny)
(ln2)
(ln2+lnx)=(ln3)(1+
lny
ln3
)
⇒(ln2)(
lny
ln2
+
lny
lnx
)=ln3(1+
lny
ln3
)(equation 1)
And 3
lnx
=2
lny
Taking ln both side,
⇒(lnx)(ln3)=(lny)(ln2)
⇒
lny
lnx
=
ln3
ln2
(equation 2)
From 1 and 2
⇒(ln2)(
lny
ln2
+
lny
lnx
)=ln3(1+
lny
ln3
)
⇒
lny
(ln2)
2
−(ln3)
2
=
ln3
(ln3)
2
(ln2)
2
⇒lny=−ln3
⇒y=
3
1
And from 1
⇒lnx=−ln2
⇒x=+
2
1
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