Whakaoti i te 25^n=100

$$25 ^ { n } = 100$$

Whakaoti mō n

$$n=\log_{5}\left(10\right)\approx 1.430676558$$

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.

$$25^{n}=100$$

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

$$\log(25^{n})=\log(100)$$

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

$$n\log(25)=\log(100)$$

Whakawehea ngā taha e rua ki te \log(25).

$$n=\frac{\log(100)}{\log(25)}$$

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

$$n=\log_{25}\left(100\right)$$

Whakaoti mō n (complex solution)

$$n=\frac{\pi n_{1}i}{\ln(5)}+\log_{5}\left(10\right)$$

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