Determinar el valor de k tal que :[tex] \ lim_{n \ to + \ infty} [ \ frac{kx - 1}{kx + 1}] ^ x = 4 [ / tex]Como ayuda : la respuesta es : k = - 2 / ln(4)Lo que me urge es saber el procedimiento correc?

<img src="https://tex.z-dn.net/?f=%5Cdisplaystyle%0A%5Clim%5Climits_%7Bx%5Cto%2B%5Cinfty%7D%5Cleft%28%5Cfrac%7Bkx-1%7D%7Bkx%2B1%7D%5Cright%29%5Ex%3D4" />

recordemos que

<img src="https://tex.z-dn.net/?f=%24%5Clim%5Climits_%7Bx%5Cto%20%2B%5Cinfty%7D%5Cleft%281%2B%5Cfrac%7B1%7D%7Bx%7D%5Cright%29%5Ex%3De%24" />

Tratemos de llevar la expresión a esa forma

<img src="https://tex.z-dn.net/?f=%5Cdisplaystyle%20%0AL%3D%5Clim%5Climits_%7Bx%5Cto%2B%5Cinfty%7D%5Cleft%28%5Cfrac%7B%28kx%2B1%29-2%7D%7Bkx%2B1%7D%5Cright%29%5Ex%5C%5C%20%5C%5C%0AL%3D%5Clim%5Climits_%7Bx%5Cto%2B%5Cinfty%7D%5Cleft%281-%5Cfrac%7B2%7D%7Bkx%2B1%7D%5Cright%29%5Ex%5C%5C%20%5C%5C%0AL%3D%5Clim%5Climits_%7Bx%5Cto%2B%5Cinfty%7D%5Cleft%281%2B%5Cfrac%7B1%7D%7B-%5Cfrac%7Bkx%2B1%7D%7B2%7D%7D%5Cright%29%5Ex%5C%5C%20%5C%5C%0AL%3D%5Clim%5Climits_%7Bx%5Cto%2B%5Cinfty%7D%5Cleft%281%2B%5Cfrac%7B1%7D%7B-%5Cfrac%7Bkx%2B1%7D%7B2%7D%7D%5Cright%29%5E%7B%5B-%28kx%2B1%29%2F2%2B1%2F2%5D%28-2%2Fk%29%7D%5C%5C%20%5C%5C%0AL%3D%5Clim%5Climits_%7Bx%5Cto%2B%5Cinfty%7D%5Cleft%281%2B%5Cfrac%7B1%7D%7B-%5Cfrac%7Bkx%2B1%7D%7B2%7D%7D%5Cright%29%5E%7B%5B-%28kx%2B1%29%2F2%5D%28-2%2Fk%29%7D%5Cleft%281%2B%5Cfrac%7B1%7D%7B-%5Cfrac%7Bkx%2B1%7D%7B2%7D%7D%5Cright%29%5E%7B-1%2Fk%7D%5C%5C%20%5C%5C%0AL%3De%5E%7B-2%2Fk%7D%281%2B0%29%5E%7B-1%2Fk%7D%20%5C%5C%20%5C%5C" />

<img src="https://tex.z-dn.net/?f=%5Cdisplaystyle%0A%5Cboxed%7BL%3De%5E%7B-2%2Fk%7D%7D%5C%5C%20%5C%5C%0Ae%5E%7B-2%2Fk%7D%3D4%5C%5C%20%5C%5C%0A-2%2Fk%20%3D%20%5Cln4%20%5C%5C%20%5C%5C%0A%5Cboxed%7Bk%3D-%5Cfrac%7B2%7D%7B%5Cln4%7D%7D" />.