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

Let (x_(0),y_(0)) be the solution of the following equations (2x)^(ln2)=(3y)^(ln3) and 3^(lnx)=2^(lny) then 2x_(0)=

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 is

Let (x_(0),y_(0)) be the solution of the following equations: (2x)^(ln2)=(3y)^(ln3) and 3^(ln x)=2^(ln y) Then value of x_(0) is:

Let (x_(0),y_(0)) be the solution of the following equations In (2x)^(In2)=(3y)^(ln3) and 3^(ln x)=2^(ln y) Then x_(0) is

If x,y(x!=1) satisfy both the equation 2^(lnx) = 3^(lny) and (ln^2 x) = (ln^3y). The value of the expression sqrt(lny)+3sqrt(lnx) can be expressed as log_b a (where a, b in N). Then find the smallest value of |a-b|.

int_(2-ln3)^(3+ln3)(ln(4+x))/(ln(4+x)+ln(9-x))dx is equal to :

int_(2-ln3)^(3+ln3)(ln(4+x))/(ln(4+x)+ln(9-x))dx is equal to :

int_(2-ln3)^(3+ln3)((ln(4+x))/(ln(4+x)+ln(9-x)dx)

If a!=1 and ln a^(2)+(ln a^(2))^(2)+(ln a^(2))^(3)+...=3(ln a+(ln a)^(2)+(ln a)^(3)+(ln a)^(4)+......) then a is equal to