Question

2x-1/x+3/4=4/x. Find x pls

Answer 1

4^x -3^(x-1/2) =3^(x+1/2) -2^(2x-1)

=> 4^x +2^(2x-1) = 3^(x-1/2) +3^(x+1/2)

2^2x +2^2x * 2^-1 = (3^x-1/2 )* 3^x + 3^(1/2)* 3^x

=> 2^2x (1+1/2) = 3^x ( 3^(-1/2) + 3^(1/2))

=> 4^x * (3/2)= 3^ x * ( 4 / sqrt(3))

=> 4^x / 3^x = 8/ (3 sqrt(3)) = 8 sqrt(3) / 9

=> (4/3)^x = 8 sqrt(3) /9

Answer 2

4^x -3^(x-1/2) =3^(x+1/2) -2^(2x-1)

=> 4^x +2^(2x-1) = 3^(x-1/2) +3^(x+1/2)

2^2x +2^2x * 2^-1 = (3^x-1/2 )* 3^x + 3^(1/2)* 3^x

=> 2^2x (1+1/2) = 3^x ( 3^(-1/2) + 3^(1/2))

=> 4^x * (3/2)= 3^ x * ( 4 / sqrt(3))

=> 4^x / 3^x = 8/ (3 sqrt(3)) = 8 sqrt(3) / 9

=> (4/3)^x = 8 sqrt(3) /9