1) calcular el valor de n si : 7 es elevada a la n por 15 elevada a la 4 , posee 100 divisores 2) hallar el valor de n si 2 es elevada a la 2n por 3 elevada a la n + 1 por 5 y n 70 divisores.
En resumen
<img src="https://tex.z-dn.net/?f=7%5E%7Bn%7D%20.15%20%5E%7B4%7D%20" /> (n + 1)(4 + 1) = 100 (n + 1)(5) = 100 <img src="https://tex.z-dn.net/?f=n%2B1%20%3D%20%20%5Cfrac%7B100%7D%7B20%7D%20" /> n + 1 = 20 n = 20 - 1 n = 19 <img src="https://tex.z-dn.net/?f=%202%5E%7B2n%7D%20.
<img src="https://tex.z-dn.net/?f=7%5E%7Bn%7D%20.15%20%5E%7B4%7D%20" />
(n + 1)(4 + 1) = 100
(n + 1)(5) = 100
<img src="https://tex.z-dn.net/?f=n%2B1%20%3D%20%20%5Cfrac%7B100%7D%7B20%7D%20" />
n + 1 = 20
n = 20 - 1
n = 19
<img src="https://tex.z-dn.net/?f=%202%5E%7B2n%7D%20.%203%5E%7Bn%2B1%7D%20.5%20%20%3D70" />
(2n + 1)(n + 1 + 1)(1 + 1) = 70
(2n + 1)(n + 2)(2) = 70
<img src="https://tex.z-dn.net/?f=2%20n%5E%7B2%7D%20%2B5n%20%2B2%20%3D%20%20%5Cfrac%7B70%7D%7B2%7D%20" />
<img src="https://tex.z-dn.net/?f=2n%5E%7B2%7D%20%2B%205n%20%2B2%20%3D%2035" />
<img src="https://tex.z-dn.net/?f=2n%5E%7B2%7D%20%2B%205n%20-33%20%3D%200" />
2n + 11
n - 3
11n - 6n = 5n
(n + 11)(n - 3) = 0
n + 11 = 0 n - 3 = 0
n = - 11 n = 3
el valor de n es 3.