1.

Let `(x_0, y_0)` be the solution of the following equations In `(2x)^(In2)=(3y)^(ln3)`and `3^(lnx)=2^(lny)` Then `x_0` isA. `(1)/(6)`B. `(1)/(3)`C. `(1)/(2)`D. 6

Answer» Correct Answer - C
We have,
`(2x)^("In"2)=(3y)^("In"3)"and",3^("In"x)=2^("In"y) `
`rArrlog(2x)^("In"2)=log(3y)^("In"3)" and "log(3^("In"x))=log(2^("In"y))`
`rArr log2(log2+logx)=log3(log+logy)`
and, `log3 logx=log2 logy`
`rArr (log2)^(2)+(log2)(logx)=(log3)^(2)+((log3)^(2)logx)/(log2)`
[On eliminating logy]
`rArr ((log2)^(2)-(log3)^(2))/(log2)logx=(log3)^(2)-(log2)^(2)`
`rArr logx=-log2 rArrx=(1)/(2)`


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