Let `(x_0,y_0)` be the solution of the following equations: `(2x)^ln2 = (3y)^ln3 and 3^(lnx) = 2^(lny)` Then value of `x_0` is:

Explanation

`(2x)^(ln2) = (3y)^ln3`

Taking `ln` both sides,

`=>(ln2) (ln2x) = (ln3)(ln3y)`

`=>(ln2) (ln2 +lnx) = (ln3)(ln3+lny)->(1)`

Now, we will take the second equation,

`3^(ln x) = 2^(ln y)`

Taking `ln` both sides,

`=>(ln x)(ln 3) = (ln y)(ln 2)`

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