Logarithm question-I donot know but this question may be solved by any other way also.Let (x_0,y_0) be the solution of the following equations. (2x)^(ln2)=(3y)^(ln3) 3^(lnx)=2^(lny) Then x_0 is A) 1/6 B) 1/3 C) 1/2 D) 6 I have tried this problem by taking log on both sides of the two equations. But, finally I could not make up to get the values of x and y.

aanpalendmw 2022-07-15 Answered
Logarithm question-I donot know but this question may be solved by any other way also.
Let ( x 0 , y 0 ) be the solution of the following equations.
( 2 x ) ln 2 = ( 3 y ) ln 3
3 ln x = 2 ln y
Then x 0 is
A) 1 6
B) 1 3
C) 1 2
D) 6
I have tried this problem by taking log on both sides of the two equations. But, finally I could not make up to get the values of x and y
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Answers (2)

wintern90
Answered 2022-07-16 Author has 12 answers
I would suggest to:
take ln on both sides of the first equation.
express ln y from the second equation and substitute it into the first equation
Now you have the equation with one variable. After rather simple transformations you will get the answer for ln x and later for x
Let me know if I'm not clear or you need further help.
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kokomocutie88r1
Answered 2022-07-17 Author has 2 answers
Note ln 2 = a , ln 3 = b , ln x = u , ln y = v .
Logarithm equations are obtained:
a 2 + a u = b 2 + b v
and
b u = a v .
With
v = b a u
find
u = a .
Conclusion:
x 0 = 1 2 .
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