Question

$5* 4^{x} -11* 6^{x}+2* 9^{x}=0$

Answer 1

5*4^x -11*(2*3)^x +2*9^x =0

5*(2^2)^x -11*(2*3)^x +2*(3^2)^x=0

5*(2^x)^2 -11*(2^x)(3^x) +2*(3^x)^2 =0

Impartim prin (2^x)(3^x)

5*[(2^x)/(3^x)] -11+2*[(3^x)/(2^x)]=0

5*(2/3)^x -11 +2*(3/2)^x =0

Notam (2/3)^x =t

5t-11+2/t=0

Inmultim cu t

5t^2 -11t+2=0

(t-2)(5t-1)=0

t=2, (2/3)^x =2, x=log in baza 2/3 din 2

t=1/5, (2/3)^x =1/5, x=log in baza 2/3 din 1/5