Whakaoti i te 239=3^n-1

$$239 = 3 ^ { n - 1 }$$

Whakaoti mō n

$$n=\log_{3}\left(239\right)+1\approx 5.984891948$$

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

Whakawhitihia ngā taha kia puta ki te taha mauī ngā kīanga tau taurangi katoa.

$$3^{n-1}=239$$

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

$$\log(3^{n-1})=\log(239)$$

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

$$\left(n-1\right)\log(3)=\log(239)$$

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

$$n-1=\frac{\log(239)}{\log(3)}$$

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

$$n-1=\log_{3}\left(239\right)$$

Me tāpiri 1 ki ngā taha e rua o te whārite.

$$n=\log_{3}\left(239\right)-\left(-1\right)$$