Whakaoti i te (7^2)^n=497^8

$$( 7 ^ { 2 } ) ^ { n } = 497 ^ { 8 }$$

Whakaoti mō n

$$n=4\log_{7}\left(497\right)\approx 12.762336491$$

Ngā Upane e Whakamahi ana i te Tautuhinga o te Taupū Kōaro

Tātaihia te 7 mā te pū o 2, kia riro ko 49.

$$49^{n}=497^{8}$$

Tātaihia te 497 mā te pū o 8, kia riro ko 3722640602679094258561.

$$49^{n}=3722640602679094258561$$

Tuhia te tau taupū kōaro o ngā taha e rua o te whārite.

$$\log(49^{n})=\log(3722640602679094258561)$$

Ko te taupū kōaro o tētahi tau ka hīkina ki tētahi pū ko te pū whakarea ki te taupū kōaro o taua tau.

$$n\log(49)=\log(3722640602679094258561)$$

Whakawehea ngā taha e rua ki te \log(49).

$$n=\frac{\log(3722640602679094258561)}{\log(49)}$$

Mā te tikanga tātai huri pūtake \frac{\log(a)}{\log(b)}=\log_{b}\left(a\right).

$$n=\log_{49}\left(3722640602679094258561\right)$$

Whakaoti mō n (complex solution)

$$n=\frac{\pi n_{1}i}{\ln(7)}+4\log_{7}\left(497\right)$$

$$n_{1}\in \mathrm{Z}$$