ln2x^ln2=ln3y^ln33^lnx=2^lnythen find the values of x and y
sri priya yadav , 5 Years ago
Grade 11
Algebra> ln2x^ln2=ln3y^ln3 3^lnx=2^lny then find t...
2 Answerskartik
Last Activity: 5 Years ago
(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
Last Activity: 3 Years ago
(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
Provide a better Answer & Earn Cool Goodies
Enter text here...
LIVE ONLINE CLASSES
Prepraring for the competition made easy just by live online class.
Full Live Access
Study Material
Live Doubts Solving
Daily Class Assignments
Ask a Doubt
Get your questions answered by the expert for free
Enter text here...
Other Related Questions on Algebra
Can we divide two vectors? If this is possible then how?
Algebra
1 Answer Available
Last Activity: 10 Month ago(s)
How do you write “the product of 18 and q” as an algebraic expression?
Algebra
1 Answer Available
Last Activity: 10 Month ago(s)
दहावीच्या आय सी एस इ विद्यार्थ्यांनी पुढे काय करायला पाहिजे
Algebra
0 Answer Available
Last Activity: 1 Year ago(s)