9 ^ x - 6×3 ^ x + 81 = 0 porfavor ayudenme con esto es caso 2 porfavor ecuacion exponensial?

Hola.

<img src="https://tex.z-dn.net/?f=9%5Ex-6%5Ccdot%20%5C%3A3%5Ex%2B81%3D0%20%20%20%5C%5C" />

Convertir 9x = <img src="https://tex.z-dn.net/?f=3%5E2" />

<img src="https://tex.z-dn.net/?f=%5Cleft%283%5E2%5Cright%29%5Ex-6%5Ccdot%20%5C%3A3%5Ex%2B81%3D0" />

<img src="https://tex.z-dn.net/?f=3%5E%7B2x%7D-6%5Ccdot%20%5C%3A3%5Ex%2B81%3D0" />

Aplicamos leyes de exponentes.

<img src="https://tex.z-dn.net/?f=a%5E%7Bbc%7D%3D%5Cleft%28a%5Eb%5Cright%29%5Ec%20" />

<img src="https://tex.z-dn.net/?f=%5Cleft%283%5Ex%5Cright%29%5E2-6%5Ccdot%20%5C%3A3%5Ex%2B81%3D0" />

Sustituimos : <img src="https://tex.z-dn.net/?f=3%5Ex%20%3D%20u" />

Reescribimos :

<img src="https://tex.z-dn.net/?f=%5Cleft%28u%5Cright%29%5E2-6u%2B81%3D0" />

Discriminante :

<img src="https://tex.z-dn.net/?f=u%5E2-6u%2B81%3D0%20%20%5C%5C%20%20%5C%5C%20%3D%20%5Cleft%28-6%5Cright%29%5E2-4%5Ccdot%20%5C%3A1%5Ccdot%20%5C%3A81%20%3D%20-288%20%5C%5C%20%20%5C%5C%20" />

<img src="https://tex.z-dn.net/?f=%5Cmathrm%7BEl%5C%3Adiscriminante%5C%3Ano%5C%3Apuede%5C%3Aser%5C%3Anegativo%5C%3Apara%5C%3A%7Du%5Cin%20%5Cmathbb%7BR%7D" />

[img = 10]

¡Espero haberte ayudado, saludos!