Necesito si ayuda porfa [tex] log x_{ \ frac{1}{4} } 1 + log _{ \ frac{2}{3} } \ frac{3}{2} + log _{3} \ frac{1}{3} [ / tex] como se resuelve : (?

Debemos resolver cada logaritmo separado utilizando la propiedad de los logaritmos la cual es :

•<img src="https://tex.z-dn.net/?f=%7B%5Clog_n%28a%29%3Db%7D%5C%5C%5C%5C%7B%5Cboxed%7Bn%5Eb%3Da%7D%7D" />

Ahora realizamos un por uno :

1.

-

<img src="https://tex.z-dn.net/?f=%7B%5Clog_%7B%5Cfrac%7B1%7D%7B4%7D%7D%281%29%3Dx%7D%5C%5C%5C%5C%7B%5Cleft%28%5Cfrac%7B1%7D%7B4%7D%5Cright%29%5Ex%3D1%7D%5C%5C%5C%5C%7B%5Cboxed%7Bx%3D0%7D%7D" />

2.

-

<img src="https://tex.z-dn.net/?f=%7B%5Clog_%7B%5Cfrac%7B2%7D%7B3%7D%7D%5Cleft%28%5Cfrac%7B3%7D%7B2%7D%5Cright%29%3Dx%7D%5C%5C%5C%5C%7B%5Cleft%28%5Cfrac%7B2%7D%7B3%7D%5Cright%29%5Ex%3D%5Cfrac%7B3%7D%7B2%7D%7D%5C%5C%5C%5C%7B%5Cleft%28%5Cfrac%7B2%7D%7B3%7D%5Cright%29%5Ex%3D%5Cleft%28%5Cfrac%7B2%7D%7B3%7D%5Cright%29%5E%7B-1%7D%7D%5C%5C%5C%5C%7B%5Cboxed%7Bx%3D-1%7D%7D" />

3.

-

<img src="https://tex.z-dn.net/?f=%7B%5Clog_%7B9%7D%5Cleft%28%5Cfrac%7B1%7D%7B3%7D%5Cright%29%3Dx%7D%5C%5C%5C%5C%7B9%5Ex%3D%5Cfrac%7B1%7D%7B3%7D%7D%5C%5C%5C%5C%7B3%5E%7B2x%7D%3D%5Cleft%28%5Cfrac%7B3%7D%7B1%7D%5Cright%29%5E%7B-1%7D%7D%5C%5C%5C%5C%7B2x%3D-1%7D%5C%5C%5C%5C%7B%5Cboxed%7Bx%3D-1%2F2%7D%7D" />

Ahora sumamos los resultados :

• 0 + ( - 1) + ( - 1 / 2) =

• 0 - 1 - 1 / 2 =

• - 3 / 2

Salu2!

: )

Wellington.