Whakaoti i te 3^n=4

$$3 ^ { n } = 4$$

Whakaoti mō n

$$n=2\log_{3}\left(2\right)\approx 1.261859507$$

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

Whakamahia ngā ture taupū me ngā taupū kōaro hei whakaoti i te whārite.

$$3^{n}=4$$

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

$$\log(3^{n})=\log(4)$$

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

$$n\log(3)=\log(4)$$

Whakawehea ngā taha e rua ki te \log(3).

$$n=\frac{\log(4)}{\log(3)}$$

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

$$n=\log_{3}\left(4\right)$$

Whakaoti mō n (complex solution)

$$n=\frac{2\pi n_{1}i}{\ln(3)}+2\log_{3}\left(2\right)$$

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