Whakaoti i te 625=1/25*5^n-1

$$625 = \frac { 1 } { 25 } \times 5 ^ { n - 1 }$$

Whakaoti mō n

$$n=7$$

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

Me whakarea ngā taha e rua ki te 25, te tau utu o \frac{1}{25}.

$$625\times 25=5^{n-1}$$

Whakareatia te 625 ki te 25, ka 15625.

$$15625=5^{n-1}$$

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

$$5^{n-1}=15625$$

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

$$\log(5^{n-1})=\log(15625)$$

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

$$\left(n-1\right)\log(5)=\log(15625)$$

Whakawehea ngā taha e rua ki te \log(5).

$$n-1=\frac{\log(15625)}{\log(5)}$$

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

$$n-1=\log_{5}\left(15625\right)$$

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

$$n=6-\left(-1\right)$$