Let (x₀, y₀ ) be the solution of the following equations (2 x)^ 2 =(3 y)^ 3 , 3^ x =2^ y , then x₀ is equal to

Step-by-step solution

Taking log on both sides, 2 (2 x)= 3( 3 y) array ll & 2 2+ x & = 3 3+ y and & x 3= y 2 & y= x 3 2 array From Eqs. (i) and (ii), we get aligned & 2 2+ x &= 3 3+ x 3 2 & ( 2)^2+ 2 x &=( 3)^2+ ( 3)^2 ( 2) x & x ( 3)^2 2 - 2 &=( 2)^2-( 3)^2 aligned aligned & x=- 2= 2⁻¹ & x= 1 2 aligned